#include <stdio.h>

struct Matrix2 {
  int m[2][2];
};

void setMatrix(struct Matrix2 *M, int a, int b, int c, int d) {
  M->m[0][0] = a;
  M->m[0][1] = b;
  M->m[1][0] = c;
  M->m[1][1] = d;
}

void setMatrixE(struct Matrix2 *M) { setMatrix(M, 1, 0, 0, 1); }

struct Matrix2 calcMatrixMul(struct Matrix2 A, struct Matrix2 B) {
  struct Matrix2 C;
  C.m[0][0] = A.m[0][0] * B.m[0][0] + A.m[0][1] * B.m[1][0];
  C.m[0][1] = A.m[0][0] * B.m[0][1] + A.m[0][1] * B.m[1][1];
  C.m[1][0] = A.m[1][0] * B.m[0][0] + A.m[1][1] * B.m[1][0];
  C.m[1][1] = A.m[1][0] * B.m[0][1] + A.m[1][1] * B.m[1][1];
  return C;
}

void vomitMatrix2(struct Matrix2 M) {
  printf("(%d, %d, %d, %d)\n",
         M.m[0][0],
         M.m[0][1],
         M.m[1][0],
         M.m[1][1]);
}

void LinearDiophantine(int a, int b, int *d, int *x, int *y) {
  struct Matrix2 M, A;
  int k, r;
  setMatrixE(&M);
  for (;;) {
    k = a / b;
    r = a % b;
    setMatrix(&A, 0, 1, 1, -k);
    M = calcMatrixMul(A, M);
/*    printf("(%d, %d) = (%d, %d) : %d\n", a, b, b, r, k); */
/*    vomitMatrix2(M); */
    if (r == 0)
      break;
    a = b;
    b = r;
  }
  *d  = b;
  *x = M.m[0][0];
  *y = M.m[0][1];
}

int main() {
  int a, b, s;
  int d, x, y;
  int t;
  printf("a = "); scanf("%d", &a); putchar('\n');
  printf("b = "); scanf("%d", &b); putchar('\n');
  printf("s = "); scanf("%d", &s); putchar('\n');
  if (a < b) { t = a; a = b; b = t; }
  LinearDiophantine(a, b, &d, &x, &y);
  printf("(%d)a + (%d)b = %d\n", x, y, d);
  if (s != d) {
    if (s % d == 0) {
      printf("(%d)a + (%d)b = %d\n", x * (s / d), y * (s / d), s);
    } else {
      printf("no solution.\n");
    }
  }  
  return 0;
}
/* end */
/* ref. http://w...content-available-to-author-only...o.jp/dp/4314001658/ chapter.1-3
 *      http://w...content-available-to-author-only...o.jp/dp/4000076345/ chapter.7(2)
 */