矩阵快速幂
按列递推
#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <algorithm>
#include <cmath>
#include <cstring>
#define ll long long
using namespace std;
const int MOD = 10000007;
int n, m;
struct Matrix {
ll num[15][15];
void clear() {
memset(num, 0, sizeof(num));
}
void unit() {
clear();
for(int i = 0; i <= n + 1; i++) num[i][i] = 1;
}
Matrix operator * (const Matrix & b) {
Matrix ans;
ans.clear();
for(int i = 0; i <= n + 1; i++) {
for(int j = 0; j <= n + 1; j++) {
ll tmp = 0ll;
for(int k = 0; k <= n + 1; k++) {
tmp += num[i][k] * b.num[k][j];
}
ans.num[i][j] = tmp % MOD;
}
}
return ans;
}
Matrix operator ^ (ll k) {
Matrix ans, tt = (*this);
ans.unit();
while(k) {
if(k & 1ll) ans = ans * tt;
tt = tt * tt;
k >>= 1;
}
return ans;
}
void print() {
for(int i = 0; i <= n + 1; i ++) {
for(int j = 0; j <= n + 1; j++) {
printf("%lld ", num[i][j]);
}
printf("\n");
}
}
};
int main() {
while(~scanf("%d %d", &n, &m)) {
Matrix a, b;
a.clear(); b.clear();
for(int i = 0; i <= n + 1; i++) {
if(i <= n) a.num[i][0] = 10;
a.num[i][n + 1] = 1;
}
for(int i = 1; i <= n; i++) {
for(int j = 1; j <= i; j++) {
a.num[i][j] = 1;
}
}
b.num[0][0] = 23; b.num[n + 1][0] = 3;
for(int i = 1; i <= n; i++) scanf("%lld", &b.num[i][0]);
b = (a ^ m) * b;
cout << b.num[n][0] << endl;
}
return 0;
}