#include<iostream>
#include<algorithm>
#include<climits>
#include<cstring>
#include<fstream>
#include<vector>
#define all(a) a.begin(), a.end()
#define fr(i, zz, zzz) for (int i = zz; i <= zzz; i++)
#define ll long long
#define pii pair<int, int>
#define frr(i, zz, zzz) for (int i = zz; i >= zzz; i--)
#define full(asdf) memset(asdf, 0, sizeof(asdf))
#define st first
#define nd second
#define IOS ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using namespace std;
const int N = 1E6+1;
int a[5005], n, k;
ll c[N], mn = LLONG_MAX;
vector<ll> res, ress;
void Try(int i, int en, int sum, vector<ll>& p) {
if (sum + (en - i)*mn > k)
return;
if (i > en) {
p.push_back(sum);
return;
}
else {
Try(i+1, en, sum + a[i], p);
Try(i+1, en, sum, p);
}
}
int main () {
IOS
fstream f,g;
f.open("FAIR.INP", ios::in);
g.open("FAIR.OUT", ios::out);
int cnt = 0;
f >> n >> k;
fr(i, 1, n) {
f >> a[i];
mn = min(mn, (ll)a[i]);
}
if (k == 0) {
g << 1;
return 0;
}
if (n <= 40) {
Try(1, n/2, 0, res);
Try(n/2+1, n, 0, ress);
/*
for (int x : res)
cout << x << " ";
cout << "\n";
for (int x : ress)
cout << x << " ";
cout << "\n";
*/
fr(i, 0, res.size() - 1) {
if (res[i] != -1) {
if (res[i] == k) {
++cnt;
res[i] = -1;
}
else {
fr(j, 0, ress.size() - 1) {
if (ress[j] != -1) {
if (ress[j] == k) {
++cnt;
ress[j] = -1;
}
else {
if (res[i] + ress[j] == k) {
++cnt;
}
}
}
}
}
}
}
g << cnt % 123456789;
return 0;
}
else {
ll s = 0;
full(c);
c[0] = 1;
fr(i, 1, n) {
if (s + a[i] < k)
s += a[i];
else
s = k;
frr(j, s, a[i]) {
if (c[j - a[i]] != 0)
c[j] = (c[j] + c[j - a[i]]) % 123456789;
}
}
g << c[k];
}
}
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