void matrix_exp(const Matrix &m, u64 e, Matrix &r)
{
if (e == 1) { r = m; return; }
Matrix x;
if (e % 2 == 0) {
matrix_exp(m, e / 2, x);
matrix_mul(x, x, r);
return;
}
matrix_exp(m, e-1, x);
matrix_mul(x, m, r);
}
int main()
{
choose_table();
int T;
scanf("%d", &T);
int ncase = 0;
while (T--) {
scanf("%llu%d", &N, &K);
if (N == 1) {
printf("Case %d: 1\n", ++ncase);
continue;
}
fill_matrices();
matrix_exp(A, N-1, R);
u32 ans = 0;
for (int i = 0; i <= K + 1; ++i)
ans += R.m[K+1][i];
printf("Case %d: %u\n", ++ncase, ans);
}
return 0;
}
/* fast exponentiation algorithm, not used anymore but could be useful in a primary test */
int* matrix_exp(int n, const int *a, int m, int *r) {
/* it would be possible to do one less allocation here
at the cost of a memmove()
but it would make the code more complicated */
int *sq, *tmp;
if (m == 0) return (matrix_make_id(n, r));
if (m == 1) return r;
sq = matrix_mult(n, a, a, malloc(n*n*sizeof(int)));
if (m % 2 == 0) {
matrix_exp(n, sq, m/2, r);
} else {
tmp = matrix_exp(n, sq, m/2, malloc(n*n*sizeof(int)));
matrix_mult(n, a, tmp, r);
free(tmp);
}
free(sq);
return r;
}
