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

 1 /**************************************************************
 2     Problem: 3288
 3     User: rausen
 4     Language: C++
 5     Result: Accepted
 6     Time:304 ms
 7     Memory:9596 kb
 8 ****************************************************************/
 9
10 #include <cstdio>
11
12 using namespace std;
13 typedef long long ll;
14 const int N = 1e6 + 5;
15 const int mod = 1e9 + 7;
16
17 int n;
18 ll ans = 1;
19 int phi[N], p[N], cnt;
20 bool f[N];
21
22 void get_phi(int N) {
23     int i, j, k;
24     for (phi[1] = 1, i = 2; i <= N; ++i) {
25         if (!f[i]) p[++cnt] = i, phi[i] = i - 1;
26         for (j = 1; j <= cnt; ++j) {
27             if ((k = i * p[j]) > N) break;
28             f[k] = 1;
29             if (i % p[j] == 0) {
30                 phi[k] = phi[i] * p[j];
31                 break;
32             }
33             phi[k] = phi[i] * (p[j] - 1);
34         }
35     }
36 }
37
38 int main() {
39     int i;
40     scanf("%d", &n);
41     get_phi(n);
42     for (i = 1; i <= n; ++i)
43         (ans *= phi[i]) %= mod;
44     printf("%lld\n", ans);
45     return 0;
46 }