#pragma GCC optimize ("Ofast")
#include<bits/stdc++.h>
using namespace std;
#define MD (1000000007U)
template<class T> struct cLtraits_identity{
using type = T;
}
;
template<class T> using cLtraits_try_make_signed =
typename conditional<
is_integral<T>::value,
make_signed<T>,
cLtraits_identity<T>
>::type;
template <class S, class T> struct cLtraits_common_type{
using tS = typename cLtraits_try_make_signed<S>::type;
using tT = typename cLtraits_try_make_signed<T>::type;
using type = typename common_type<tS,tT>::type;
}
;
void*wmem;
char memarr[96000000];
template<class S, class T> inline auto min_L(S a, T b)
-> typename cLtraits_common_type<S,T>::type{
return (typename cLtraits_common_type<S,T>::type) a <= (typename cLtraits_common_type<S,T>::type) b ? a : b;
}
template<class T> inline void walloc1d(T **arr, int x, void **mem = &wmem){
static int skip[16] = {0, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1};
(*mem) = (void*)( ((char*)(*mem)) + skip[((unsigned long long)(*mem)) & 15] );
(*arr)=(T*)(*mem);
(*mem)=((*arr)+x);
}
template<class T> inline void walloc1d(T **arr, int x1, int x2, void **mem = &wmem){
walloc1d(arr, x2-x1, mem);
(*arr) -= x1;
}
struct Modint{
unsigned val;
Modint(){
val=0;
}
Modint(int a){
val = ord(a);
}
Modint(unsigned a){
val = ord(a);
}
Modint(long long a){
val = ord(a);
}
Modint(unsigned long long a){
val = ord(a);
}
inline unsigned ord(unsigned a){
return a%MD;
}
inline unsigned ord(int a){
a %= (int)MD;
if(a < 0){
a += MD;
}
return a;
}
inline unsigned ord(unsigned long long a){
return a%MD;
}
inline unsigned ord(long long a){
a %= (int)MD;
if(a < 0){
a += MD;
}
return a;
}
inline unsigned get(){
return val;
}
inline Modint &operator++(){
val++;
if(val >= MD){
val -= MD;
}
return *this;
}
inline Modint &operator--(){
if(val == 0){
val = MD - 1;
}
else{
--val;
}
return *this;
}
inline Modint operator++(int a){
Modint res(*this);
val++;
if(val >= MD){
val -= MD;
}
return res;
}
inline Modint operator--(int a){
Modint res(*this);
if(val == 0){
val = MD - 1;
}
else{
--val;
}
return res;
}
inline Modint &operator+=(Modint a){
val += a.val;
if(val >= MD){
val -= MD;
}
return *this;
}
inline Modint &operator-=(Modint a){
if(val < a.val){
val = val + MD - a.val;
}
else{
val -= a.val;
}
return *this;
}
inline Modint &operator*=(Modint a){
val = ((unsigned long long)val*a.val)%MD;
return *this;
}
inline Modint &operator/=(Modint a){
return *this *= a.inverse();
}
inline Modint operator+(Modint a){
return Modint(*this)+=a;
}
inline Modint operator-(Modint a){
return Modint(*this)-=a;
}
inline Modint operator*(Modint a){
return Modint(*this)*=a;
}
inline Modint operator/(Modint a){
return Modint(*this)/=a;
}
inline Modint operator+(int a){
return Modint(*this)+=Modint(a);
}
inline Modint operator-(int a){
return Modint(*this)-=Modint(a);
}
inline Modint operator*(int a){
return Modint(*this)*=Modint(a);
}
inline Modint operator/(int a){
return Modint(*this)/=Modint(a);
}
inline Modint operator+(long long a){
return Modint(*this)+=Modint(a);
}
inline Modint operator-(long long a){
return Modint(*this)-=Modint(a);
}
inline Modint operator*(long long a){
return Modint(*this)*=Modint(a);
}
inline Modint operator/(long long a){
return Modint(*this)/=Modint(a);
}
inline Modint operator-(void){
Modint res;
if(val){
res.val=MD-val;
}
else{
res.val=0;
}
return res;
}
inline operator bool(void){
return val!=0;
}
inline operator int(void){
return get();
}
inline operator long long(void){
return get();
}
inline Modint inverse(){
int a = val;
int b = MD;
int u = 1;
int v = 0;
int t;
Modint res;
while(b){
t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
if(u < 0){
u += MD;
}
res.val = u;
return res;
}
inline Modint pw(unsigned long long b){
Modint a(*this);
Modint res;
res.val = 1;
while(b){
if(b&1){
res *= a;
}
b >>= 1;
a *= a;
}
return res;
}
inline bool operator==(int a){
return ord(a)==val;
}
inline bool operator!=(int a){
return ord(a)!=val;
}
}
;
inline Modint operator+(int a, Modint b){
return Modint(a)+=b;
}
inline Modint operator-(int a, Modint b){
return Modint(a)-=b;
}
inline Modint operator*(int a, Modint b){
return Modint(a)*=b;
}
inline Modint operator/(int a, Modint b){
return Modint(a)/=b;
}
inline Modint operator+(long long a, Modint b){
return Modint(a)+=b;
}
inline Modint operator-(long long a, Modint b){
return Modint(a)-=b;
}
inline Modint operator*(long long a, Modint b){
return Modint(a)*=b;
}
inline Modint operator/(long long a, Modint b){
return Modint(a)/=b;
}
inline int my_getchar_unlocked(){
static char buf[1048576];
static int s = 1048576;
static int e = 1048576;
if(s == e && e == 1048576){
e = fread_unlocked(buf, 1, 1048576, stdin);
s = 0;
}
if(s == e){
return EOF;
}
return buf[s++];
}
inline void rd(int &x){
int k;
int m=0;
x=0;
for(;;){
k = my_getchar_unlocked();
if(k=='-'){
m=1;
break;
}
if('0'<=k&&k<='9'){
x=k-'0';
break;
}
}
for(;;){
k = my_getchar_unlocked();
if(k<'0'||k>'9'){
break;
}
x=x*10+k-'0';
}
if(m){
x=-x;
}
}
inline void rd(long long &x){
int k;
int m=0;
x=0;
for(;;){
k = my_getchar_unlocked();
if(k=='-'){
m=1;
break;
}
if('0'<=k&&k<='9'){
x=k-'0';
break;
}
}
for(;;){
k = my_getchar_unlocked();
if(k<'0'||k>'9'){
break;
}
x=x*10+k-'0';
}
if(m){
x=-x;
}
}
inline int rd_int(void){
int x;
rd(x);
return x;
}
struct MY_WRITER{
char buf[1048576];
int s;
int e;
MY_WRITER(){
s = 0;
e = 1048576;
}
~MY_WRITER(){
if(s){
fwrite_unlocked(buf, 1, s, stdout);
}
}
}
;
MY_WRITER MY_WRITER_VAR;
void my_putchar_unlocked(int a){
if(MY_WRITER_VAR.s == MY_WRITER_VAR.e){
fwrite_unlocked(MY_WRITER_VAR.buf, 1, MY_WRITER_VAR.s, stdout);
MY_WRITER_VAR.s = 0;
}
MY_WRITER_VAR.buf[MY_WRITER_VAR.s++] = a;
}
inline void wt_L(char a){
my_putchar_unlocked(a);
}
inline void wt_L(int x){
int s=0;
int m=0;
char f[10];
if(x<0){
m=1;
x=-x;
}
while(x){
f[s++]=x%10;
x/=10;
}
if(!s){
f[s++]=0;
}
if(m){
my_putchar_unlocked('-');
}
while(s--){
my_putchar_unlocked(f[s]+'0');
}
}
inline void wt_L(unsigned x){
int s=0;
char f[10];
while(x){
f[s++]=x%10;
x/=10;
}
if(!s){
f[s++]=0;
}
while(s--){
my_putchar_unlocked(f[s]+'0');
}
}
inline void wt_L(long long x){
int s=0;
int m=0;
char f[20];
if(x<0){
m=1;
x=-x;
}
while(x){
f[s++]=x%10;
x/=10;
}
if(!s){
f[s++]=0;
}
if(m){
my_putchar_unlocked('-');
}
while(s--){
my_putchar_unlocked(f[s]+'0');
}
}
inline void wt_L(unsigned long long x){
int s=0;
char f[21];
while(x){
f[s++]=x%10;
x/=10;
}
if(!s){
f[s++]=0;
}
while(s--){
my_putchar_unlocked(f[s]+'0');
}
}
inline void wt_L(Modint x){
int i;
i = (int)x;
wt_L(i);
}
int WRITER_DOUBLE_DIGIT = 15;
inline int writerDigit_double(){
return WRITER_DOUBLE_DIGIT;
}
inline void writerDigit_double(int d){
WRITER_DOUBLE_DIGIT = d;
}
inline void wt_L(double x){
const int d = WRITER_DOUBLE_DIGIT;
int k;
int r;
double v;
if(x!=x || (x==x+1 && x==2*x)){
my_putchar_unlocked('E');
my_putchar_unlocked('r');
my_putchar_unlocked('r');
return;
}
if(x < 0){
my_putchar_unlocked('-');
x = -x;
}
x += 0.5 * pow(0.1, d);
r = 0;
v = 1;
while(x >= 10*v){
v *= 10;
r++;
}
while(r >= 0){
r--;
k = floor(x / v);
if(k >= 10){
k = 9;
}
if(k <= -1){
k = 0;
}
x -= k * v;
v *= 0.1;
my_putchar_unlocked(k + '0');
}
if(d > 0){
my_putchar_unlocked('.');
v = 1;
for(r=(0);r<(d);r++){
v *= 0.1;
k = floor(x / v);
if(k >= 10){
k = 9;
}
if(k <= -1){
k = 0;
}
x -= k * v;
my_putchar_unlocked(k + '0');
}
}
}
inline void wt_L(const char c[]){
int i=0;
for(i=0;c[i]!='\0';i++){
my_putchar_unlocked(c[i]);
}
}
inline void wt_L(string &x){
int i=0;
for(i=0;x[i]!='\0';i++){
my_putchar_unlocked(x[i]);
}
}
template<class S, class T> inline S chmax(S &a, T b){
if(a<b){
a=b;
}
return a;
}
template<class T> struct Comb{
int mem_fact;
T*factri;
T*ifactri;
int mem_dfact;
T*dfactri;
int mem_pw2;
int mem_pw3;
int mem_pw10;
int mem_rep1;
T*pw2c;
T*pw3c;
T*pw10c;
T*rep1c;
int mem_ipw2;
int mem_ipw3;
int mem_ipw10;
T*ipw2c;
T*ipw3c;
T*ipw10c;
Comb(){
mem_fact = 0;
mem_dfact = 0;
mem_pw2 = mem_pw3 = mem_pw10 = mem_rep1 = 0;
mem_ipw2 = mem_ipw3 = mem_ipw10 = 0;
}
inline void expand_fact(int k){
int i;
if(k <= mem_fact){
return;
}
chmax(k, 2 * mem_fact);
if(mem_fact == 0){
factri = (T*)malloc(k * sizeof(T));
ifactri = (T*)malloc(k * sizeof(T));
factri[0] = 1;
for(i=(1);i<(k);i++){
factri[i] = i * factri[i-1];
}
ifactri[k-1] = 1 / factri[k-1];
for(i=(k-1)-1;i>=(0);i--){
ifactri[i] = (i+1) * ifactri[i+1];
}
}
else{
factri = (T*)realloc(factri, k * sizeof(T));
ifactri = (T*)realloc(ifactri, k * sizeof(T));
for(i=(mem_fact);i<(k);i++){
factri[i] = i * factri[i-1];
}
ifactri[k-1] = 1 / factri[k-1];
for(i=(k-1)-1;i>=(mem_fact);i--){
ifactri[i] = (i+1) * ifactri[i+1];
}
}
mem_fact = k;
}
inline T fac(int k){
if(mem_fact < k+1){
expand_fact(k+1);
}
return factri[k];
}
inline T ifac(int k){
if(mem_fact < k+1){
expand_fact(k+1);
}
return ifactri[k];
}
inline T C(int a, int b){
if(b < 0 || b > a){
return 0;
}
if(mem_fact < a+1){
expand_fact(a+1);
}
return factri[a] * ifactri[b] * ifactri[a-b];
}
inline T P(int a, int b){
if(b < 0 || b > a){
return 0;
}
if(mem_fact < a+1){
expand_fact(a+1);
}
return factri[a] * ifactri[a-b];
}
inline T H(int a, int b){
if(a==0 && b==0){
return 1;
}
if(a <= 0 || b < 0){
return 0;
}
if(mem_fact < a+b){
expand_fact(a+b);
}
return C(a+b-1, b);
}
inline T Multinomial(int sz, int a[]){
int i;
int s = 0;
T res;
for(i=(0);i<(sz);i++){
s += a[i];
}
if(mem_fact < s+1){
expand_fact(s+1);
}
res = factri[s];
for(i=(0);i<(sz);i++){
res *= ifactri[a[i]];
}
return 1;
}
inline T Multinomial(int a){
return 1;
}
inline T Multinomial(int a, int b){
if(mem_fact < a+b+1){
expand_fact(a+b+1);
}
return factri[a+b] * ifactri[a] * ifactri[b];
}
inline T Multinomial(int a, int b, int c){
if(mem_fact < a+b+c+1){
expand_fact(a+b+c+1);
}
return factri[a+b+c] * ifactri[a] * ifactri[b] * ifactri[c];
}
inline T Multinomial(int a, int b, int c, int d){
if(mem_fact < a+b+c+d+1){
expand_fact(a+b+c+d+1);
}
return factri[a+b+c+d] * ifactri[a] * ifactri[b] * ifactri[c] * ifactri[d];
}
inline T Catalan(int n){
if(n < 0){
return 0;
}
if(mem_fact < 2*n+1){
expand_fact(2*n+1);
}
return factri[2*n] * ifactri[n] * ifactri[n+1];
}
inline T C_s(long long a, long long b){
long long i;
T res;
if(b < 0 || b > a){
return 0;
}
if(b > a - b){
b = a - b;
}
res = 1;
for(i=(0);i<(b);i++){
res *= a - i;
res /= i + 1;
}
return res;
}
inline T P_s(long long a, long long b){
long long i;
T res;
if(b < 0 || b > a){
return 0;
}
res = 1;
for(i=(0);i<(b);i++){
res *= a - i;
}
return res;
}
inline T per_s(long long n, long long k){
T d;
int m;
if(n < 0 || k < 0){
return 0;
}
if(n == k && k == 0){
return 1;
}
if(n == 0 || k == 0){
return 0;
}
if(k==1){
return 1;
}
if(k==2){
d = n / 2;
return d;
}
if(k==3){
d = (n-1) / 6;
m = (n-1) % 6;
if(m==0){
return 3 * d * d + d;
}
if(m==1){
return 3 * d * d + 2 * d;
}
if(m==2){
return 3 * d * d + 3 * d + 1;
}
if(m==3){
return 3 * d * d + 4 * d + 1;
}
if(m==4){
return 3 * d * d + 5 * d + 2;
}
if(m==5){
return 3 * d * d + 6 * d + 3;
}
}
assert(0 && "per_s should be k <= 3");
return -1;
}
inline void expand_dfact(int k){
int i;
if(k <= mem_dfact){
return;
}
chmax(k, 3);
chmax(k, 2 * mem_dfact);
if(mem_dfact==0){
dfactri = (T*)malloc(k * sizeof(T));
dfactri[0] = dfactri[1] = 1;
for(i=(2);i<(k);i++){
dfactri[i] = i * dfactri[i-2];
}
}
else{
dfactri = (T*)realloc(dfactri, k * sizeof(T));
for(i=(mem_dfact);i<(k);i++){
dfactri[i] = i * dfactri[i-2];
}
}
mem_dfact = k;
}
inline void expand_pw2(int k){
int i;
if(k <= mem_pw2){
return;
}
chmax(k, 2 * mem_pw2);
if(mem_pw2==0){
pw2c = (T*)malloc(k * sizeof(T));
pw2c[0] = 1;
for(i=(1);i<(k);i++){
pw2c[i] = 2 * pw2c[i-1];
}
}
else{
pw2c = (T*)realloc(pw2c, k * sizeof(T));
for(i=(mem_pw2);i<(k);i++){
pw2c[i] = 2 * pw2c[i-1];
}
}
mem_pw2 = k;
}
inline void expand_ipw2(int k){
int i;
if(k <= mem_ipw2){
return;
}
chmax(k, 2);
chmax(k, 2 * mem_ipw2);
if(mem_ipw2==0){
ipw2c = (T*)malloc(k * sizeof(T));
ipw2c[0] = 1;
ipw2c[1] = ipw2c[0] / 2;
for(i=(1);i<(k);i++){
ipw2c[i] = ipw2c[1] * ipw2c[i-1];
}
}
else{
ipw2c = (T*)realloc(ipw2c, k * sizeof(T));
for(i=(mem_ipw2);i<(k);i++){
ipw2c[i] = ipw2c[1] * ipw2c[i-1];
}
}
mem_ipw2 = k;
}
inline void expand_pw3(int k){
int i;
if(k <= mem_pw3){
return;
}
chmax(k, 2 * mem_pw3);
if(mem_pw3==0){
pw3c = (T*)malloc(k * sizeof(T));
pw3c[0] = 1;
for(i=(1);i<(k);i++){
pw3c[i] = 3 * pw3c[i-1];
}
}
else{
pw3c = (T*)realloc(pw3c, k * sizeof(T));
for(i=(mem_pw3);i<(k);i++){
pw3c[i] = 3 * pw3c[i-1];
}
}
mem_pw3 = k;
}
inline void expand_ipw3(int k){
int i;
if(k <= mem_ipw3){
return;
}
chmax(k, 2);
chmax(k, 2 * mem_ipw3);
if(mem_ipw3==0){
ipw3c = (T*)malloc(k * sizeof(T));
ipw3c[0] = 1;
ipw3c[1] = ipw3c[0] / 3;
for(i=(1);i<(k);i++){
ipw3c[i] = ipw3c[1] * ipw3c[i-1];
}
}
else{
ipw3c = (T*)realloc(ipw3c, k * sizeof(T));
for(i=(mem_ipw3);i<(k);i++){
ipw3c[i] = ipw3c[1] * ipw3c[i-1];
}
}
mem_ipw3 = k;
}
inline void expand_pw10(int k){
int i;
if(k <= mem_pw10){
return;
}
chmax(k, 2 * mem_pw10);
if(mem_pw10==0){
pw10c = (T*)malloc(k * sizeof(T));
pw10c[0] = 1;
for(i=(1);i<(k);i++){
pw10c[i] = 10 * pw10c[i-1];
}
}
else{
pw10c = (T*)realloc(pw10c, k * sizeof(T));
for(i=(mem_pw10);i<(k);i++){
pw10c[i] = 10 * pw10c[i-1];
}
}
mem_pw10 = k;
}
inline void expand_ipw10(int k){
int i;
if(k <= mem_ipw10){
return;
}
chmax(k, 2);
chmax(k, 2 * mem_ipw10);
if(mem_ipw10==0){
ipw10c = (T*)malloc(k * sizeof(T));
ipw10c[0] = 1;
ipw10c[1] = ipw10c[0] / 10;
for(i=(1);i<(k);i++){
ipw10c[i] = ipw10c[1] * ipw10c[i-1];
}
}
else{
ipw10c = (T*)realloc(ipw10c, k * sizeof(T));
for(i=(mem_ipw10);i<(k);i++){
ipw10c[i] = ipw10c[1] * ipw10c[i-1];
}
}
mem_ipw10 = k;
}
inline void expand_rep1(int k){
int i;
if(k <= mem_rep1){
return;
}
chmax(k, 2 * mem_rep1);
if(mem_rep1==0){
rep1c = (T*)malloc(k * sizeof(T));
rep1c[0] = 0;
for(i=(1);i<(k);i++){
rep1c[i] = 10 * rep1c[i-1] + 1;
}
}
else{
rep1c = (T*)realloc(rep1c, k * sizeof(T));
for(i=(mem_rep1);i<(k);i++){
rep1c[i] = 10 * rep1c[i-1] + 1;
}
}
mem_rep1 = k;
}
inline T dfac(int k){
if(k >= 0){
if(mem_dfact < k+1){
expand_dfact(k+1);
}
return dfactri[k];
}
if(k==-1){
return 1;
}
k = - k - 2;
if(k % 4 == 1){
return 1 / (-dfac(k));
}
return 1 / dfac(k);
}
inline T pw2(int k){
if(k >= 0){
if(mem_pw2 < k+1){
expand_pw2(k+1);
}
return pw2c[k];
}
else{
k = -k;
if(mem_ipw2 < k+1){
expand_ipw2(k+1);
}
return ipw2c[k];
}
}
inline T pw3(int k){
if(k >= 0){
if(mem_pw3 < k+1){
expand_pw3(k+1);
}
return pw3c[k];
}
else{
k = -k;
if(mem_ipw3 < k+1){
expand_ipw3(k+1);
}
return ipw3c[k];
}
}
inline T pw10(int k){
if(k >= 0){
if(mem_pw10 < k+1){
expand_pw10(k+1);
}
return pw10c[k];
}
else{
k = -k;
if(mem_ipw10 < k+1){
expand_ipw10(k+1);
}
return ipw10c[k];
}
}
inline T repunit(int k){
if(mem_rep1 < k+1){
expand_rep1(k+1);
}
return rep1c[k];
}
}
;
template<> inline Modint Comb<Modint>::C_s(long long a, long long b){
long long i;
Modint res;
Modint d;
if(b < 0 || b > a){
return 0;
}
if(b > a - b){
b = a - b;
}
res = d = 1;
for(i=(0);i<(b);i++){
res *= a - i;
d *= i + 1;
}
return res / d;
}
template<class T> struct segtree{
int N;
int logN;
T*sum;
T*mn;
int*mnind;
T*fixval;
char*fixed;
T*addval;
void malloc(int maxN, int once = 0){
int i;
for(i=1;i<maxN;i*=2){
;
}
sum = new T[2*i];
mn = new T[2*i];
mnind = new int[2*i];
fixval = new T[i];
addval = new T[i];
fixed = new char[i];
if(once){
setN(maxN);
}
}
void walloc(int maxN, int once = 0, void **mem = &wmem){
int i;
for(i=1;i<maxN;i*=2){
;
}
walloc1d(&sum, 2*i, mem);
walloc1d(&mn, 2*i, mem);
walloc1d(&mnind, 2*i, mem);
walloc1d(&fixval, i, mem);
walloc1d(&addval, i, mem);
walloc1d(&fixed, i, mem);
if(once){
setN(maxN);
}
}
void free(void){
delete [] sum;
delete [] mn;
delete [] mnind;
delete [] fixval;
delete [] addval;
delete [] fixed;
}
T& operator[](int i){
return sum[N+i];
}
void setN(int n, int zerofill = 1, int dobuild = 1){
int i;
for(i=1,logN=0;i<n;i*=2,logN++){
;
}
N = i;
if(zerofill){
for(i=(0);i<(N);i++){
sum[N+i] = 0;
}
}
if(dobuild){
build();
}
}
void build(void){
int i;
for(i=(0);i<(N);i++){
mn[N+i] = sum[N+i];
mnind[N+i] = i;
}
for(i=N-1;i;i--){
sum[i] = sum[2*i] + sum[2*i+1];
if(mn[2*i] <= mn[2*i+1]){
mn[i] = mn[2*i];
mnind[i] = mnind[2*i];
}
else{
mn[i] = mn[2*i+1];
mnind[i] = mnind[2*i+1];
}
}
int g65CQCoC = N;
for(i=(1);i<(g65CQCoC);i++){
fixed[i] = 0;
}
int emd5LSgV = N;
for(i=(1);i<(emd5LSgV);i++){
addval[i] = 0;
}
}
inline void push_one(int a, int sz, int st){
if(fixed[a]){
if(sz > 1){
fixed[a*2] = fixed[a*2+1] = 1;
fixval[a*2] = fixval[a*2+1] = fixval[a];
sum[a*2] = sum[a*2+1] = sz * fixval[a];
mn[a*2] = mn[a*2+1] = fixval[a];
mnind[a*2] = st;
mnind[a*2+1] = st + sz;
}
else{
sum[a*2] = sum[a*2+1] = sz * fixval[a];
mn[a*2] = mn[a*2+1] = fixval[a];
mnind[a*2] = st;
mnind[a*2+1] = st + sz;
}
fixed[a] = 0;
addval[a] = 0;
return;
}
if(addval[a] != 0){
if(sz > 1){
if(fixed[a*2]){
fixval[a*2] += addval[a];
}
else{
addval[a*2] += addval[a];
}
if(fixed[a*2+1]){
fixval[a*2+1] += addval[a];
}
else{
addval[a*2+1] += addval[a];
}
sum[a*2] += sz * addval[a];
sum[a*2+1] += sz * addval[a];
mn[a*2] += addval[a];
mn[a*2+1] += addval[a];
}
else{
sum[a*2] += sz * addval[a];
sum[a*2+1] += sz * addval[a];
mn[a*2] += addval[a];
mn[a*2+1] += addval[a];
}
addval[a] = 0;
return;
}
}
inline void push(int a){
int i;
int aa = a - N;
int nd;
int sz;
int st;
for(i=logN;i;i--){
nd = a>>i;
sz = 1<<(i-1);
st = 2 * sz * (aa>>i);
push_one(nd, sz, st);
}
}
inline void build(int a){
int sz = 1;
int st = a - N;
while(a > 1){
if(a%2){
st += sz;
}
a /= 2;
sz *= 2;
if(fixed[a]){
sum[a] = sz * fixval[a];
mn[a] = fixval[a];
}
else{
sum[a] = sum[a*2] + sum[a*2+1];
if(mn[a*2] <= mn[a*2+1]){
mn[a] = mn[a*2];
mnind[a] = mnind[a*2];
}
else{
mn[a] = mn[a*2+1];
mnind[a] = mnind[a*2+1];
}
if(addval[a] != 0){
mn[a] += addval[a];
sum[a] += sz * addval[a];
}
}
}
}
inline void change(int a, int b, T val){
int sz = 1;
int aa;
int bb;
int st_a = a;
int st_b = b;
if(a >= b){
return;
}
aa = (a += N);
bb = (b += N);
push(a);
push(b-1);
if(a%2){
sum[a] = mn[a] = val;
a++;
st_a += sz;
}
if(b%2){
b--;
st_b -= sz;
sum[b] = mn[b] = val;
}
a /= 2;
b /= 2;
while(a < b){
sz *= 2;
if(a%2){
fixed[a]=1;
fixval[a]=val;
sum[a] = sz * val;
mn[a] = val;
mnind[a] = st_a;
a++;
st_a += sz;
}
if(b%2){
b--;
st_b -= sz;
fixed[b]=1;
fixval[b]=val;
sum[b] = sz * val;
mn[b] = val;
mnind[b] = st_b;
}
a /= 2;
b /= 2;
}
build(aa);
build(bb-1);
}
inline void add(int a, int b, T val){
int sz = 1;
int aa;
int bb;
if(a >= b){
return;
}
aa = (a += N);
bb = (b += N);
push(a);
push(b-1);
if(a%2){
sum[a] += val;
mn[a] += val;
a++;
}
if(b%2){
b--;
sum[b] += val;
mn[b] += val;
}
a /= 2;
b /= 2;
while(a < b){
sz *= 2;
if(a%2){
if(fixed[a]){
fixval[a] += val;
}
else{
addval[a] += val;
}
sum[a] += sz * val;
mn[a] += val;
a++;
}
if(b%2){
b--;
if(fixed[b]){
fixval[b] += val;
}
else{
addval[b] += val;
}
sum[b] += sz * val;
mn[b] += val;
}
a /= 2;
b /= 2;
}
build(aa);
build(bb-1);
}
inline pair<T,int> getMin(int a, int b){
pair<T,int> res;
pair<T,int> tmp;
int fga = 0;
int fgb = 0;
a += N;
b += N;
push(a);
push(b-1);
while(a < b){
if(a%2){
if(fga){
res =min_L(res, make_pair(mn[a], mnind[a]));
}
else{
res = make_pair(mn[a], mnind[a]);
fga = 1;
}
a++;
}
if(b%2){
b--;
if(fgb){
tmp =min_L(make_pair(mn[b], mnind[b]), tmp);
}
else{
tmp = make_pair(mn[b], mnind[b]);
fgb = 1;
}
}
a /= 2;
b /= 2;
}
if(fga==1 && fgb==0){
return res;
}
if(fga==0 && fgb==1){
return tmp;
}
if(fga==1 && fgb==1){
res =min_L(res, tmp);
return res;
}
return res;
}
inline T getMinVal(int a, int b){
T res;
T tmp;
int fga = 0;
int fgb = 0;
a += N;
b += N;
push(a);
push(b-1);
while(a < b){
if(a%2){
if(fga){
res =min_L(res, mn[a]);
}
else{
res = mn[a];
fga = 1;
}
a++;
}
if(b%2){
b--;
if(fgb){
tmp =min_L(mn[b], tmp);
}
else{
tmp = mn[b];
fgb = 1;
}
}
a /= 2;
b /= 2;
}
if(fga==1 && fgb==0){
return res;
}
if(fga==0 && fgb==1){
return tmp;
}
if(fga==1 && fgb==1){
res =min_L(res, tmp);
return res;
}
return res;
}
inline int getMinInd(int a, int b){
return getMin(a,b).second;
}
inline T getSum(int a, int b){
T res;
T tmp;
int fga = 0;
int fgb = 0;
a += N;
b += N;
push(a);
push(b-1);
while(a < b){
if(a%2){
if(fga){
res = res + sum[a];
}
else{
res = sum[a];
fga = 1;
}
a++;
}
if(b%2){
b--;
if(fgb){
tmp = sum[b] + tmp;
}
else{
tmp = sum[b];
fgb = 1;
}
}
a /= 2;
b /= 2;
}
if(fga==1 && fgb==0){
return res;
}
if(fga==0 && fgb==1){
return tmp;
}
if(fga==1 && fgb==1){
res = res + tmp;
return res;
}
return res;
}
}
;
int TEST;
int N;
long long A[100000+1];
Comb<Modint> c;
segtree<long long> t;
Modint solve(int x, int y){
int z;
if(x >= y){
return 1;
}
z = t.getMinInd(x, y);
return solve(x,z) * solve(z+1,y) * c.C(y-x-1, z-x);
}
int main(){
wmem = memarr;
t.walloc(100000+1);
int Lj4PdHRW = rd_int();
for(TEST=(0);TEST<(Lj4PdHRW);TEST++){
int i;
wt_L("Case #");
wt_L(TEST+1);
wt_L(": ");
rd(N);
{
int e98WHCEY;
for(e98WHCEY=(0);e98WHCEY<(N);e98WHCEY++){
rd(A[e98WHCEY]);
}
}
for(i=(1);i<(N);i++){
if(A[i] > A[i-1]+1){
wt_L(0);
wt_L('\n');
goto KL2GvlyY;
}
}
t.setN(N);
for(i=(0);i<(N);i++){
t[i] = A[i] * 1000000000 - i;
}
t.build();
wt_L(solve(0, N));
wt_L('\n');
KL2GvlyY:;
}
return 0;
}
// cLay version 20210405-1
// --- original code ---
// int TEST;
// int N; ll A[1d5+1];
// Comb<Modint> c;
// segtree<ll> t;
//
// Modint solve(int x, int y){
// int z;
// if(x >= y) return 1;
// z = t.getMinInd(x, y);
// return solve(x,z) * solve(z+1,y) * c.C(y-x-1, z-x);
// }
//
// {
// t.walloc(1d5+1);
// REP(TEST,rd_int()){
// wtF("Case #{TEST+1}: ");
// rd(N,A(N));
// rep(i,1,N) if(A[i] > A[i-1]+1) wt(0), break_continue;
// t.setN(N);
// rep(i,N) t[i] = A[i] * 1d9 - i;
// t.build();
// wt(solve(0, N));
// }
// }