BZOJ3288 Mato矩阵

网上说高斯消元得到下三角矩阵然后都是phi(i)...反着我是搞不出来

打个表什么的还是能看出来点奇怪的东西，比如后面能整除前面的，然后再乱搞吧2333

/**************************************************************
    Problem: 3288
    User: rausen
    Language: C++
    Result: Accepted
    Time:304 ms
    Memory:9596 kb
****************************************************************/
 
#include <cstdio>
 
using namespace std;
typedef long long ll;
const int N = 1e6 + 5;
const int mod = 1e9 + 7;
 
int n;
ll ans = 1;
int phi[N], p[N], cnt;
bool f[N];
 
void get_phi(int N) {
    int i, j, k;
    for (phi[1] = 1, i = 2; i <= N; ++i) {
        if (!f[i]) p[++cnt] = i, phi[i] = i - 1;
        for (j = 1; j <= cnt; ++j) {
            if ((k = i * p[j]) > N) break;
            f[k] = 1;
            if (i % p[j] == 0) {
                phi[k] = phi[i] * p[j];
                break;
            }
            phi[k] = phi[i] * (p[j] - 1);
        }
    }
}
 
int main() {
    int i;
    scanf("%d", &n);
    get_phi(n);
    for (i = 1; i <= n; ++i)
        (ans *= phi[i]) %= mod;
    printf("%lld
", ans);
    return 0;
}