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 + ;
 const int mod = 1e9 + ;

 int n;
 ll ans = ;
 int phi[N], p[N], cnt;
 bool f[N];

 void get_phi(int N) {
     int i, j, k;
     for (phi[] = , i = ; i <= N; ++i) {
         if (!f[i]) p[++cnt] = i, phi[i] = i - ;
         for (j = ; j <= cnt; ++j) {
             if ((k = i * p[j]) > N) break;
             f[k] = ;
             if (i % p[j] == ) {
                 phi[k] = phi[i] * p[j];
                 break;
             }
             phi[k] = phi[i] * (p[j] - );
         }
     }
 }

 int main() {
     int i;
     scanf("%d", &n);
     get_phi(n);
     for (i = ; i <= n; ++i)
         (ans *= phi[i]) %= mod;
     printf("%lld\n", ans);
     return ;
 }