mirror of
https://github.com/Kiritow/OJ-Problems-Source.git
synced 2024-03-22 13:11:29 +08:00
77 lines
2.2 KiB
C++
77 lines
2.2 KiB
C++
#include <stdio.h>
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#include <string.h>
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#include <algorithm>
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#define MAXN 20010
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int MOD;
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using namespace std;
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typedef long long LL;
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int cas, n, m, tx;
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int pri[MAXN], notp[MAXN], flag[MAXN], prs;
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int tot[MAXN], maxm;
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int fac[MAXN][305], facs[MAXN], phi[MAXN * 10];
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void init(){
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for (int i = 2; i < MAXN; i++) if (!notp[i]) {
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flag[i] = 1;
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for (int j = i*2; j < MAXN; j += i) {
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if (!notp[j]) notp[j] = flag[j] = 1;
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else if (flag[j]) flag[j]++;
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if (j%(i*i) == 0) flag[j] = 0;
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}
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}
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for (int i = 2; i < MAXN; i++)
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if (!notp[i]) pri[prs++] = i;
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for (int i = 1; i < MAXN; i++)
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for (int j = 1; j * j <= i; j++) if (i % j == 0) {
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fac[i][facs[i]++] = j;
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if (j * j != i)fac[i][facs[i]++] = i/j;
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}
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const int maxn = 100000;
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for (int i = 1; i <= maxn; i ++) phi[i] = i;
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for (int i = 2; i <= maxn; i ++) if(phi[i] == i) {
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for(int j = i; j <= maxn; j += i)
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phi[j] = phi[j] / i * (i - 1);
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}
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}
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int powmod(int x, int d){
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int ans = 1, tmp = x;
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for (; d; d >>= 1, tmp = (LL)tmp * tmp % MOD)
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if (d&1) ans = (LL)ans * tmp % MOD;
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return ans;
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}
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int cal(int l){
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int ans = powmod(tot[1], l);
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for (int i = 2; i <= maxm; i++) {
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if (flag[i] == 0) continue;
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if (flag[i] & 1) ans = (ans - powmod(tot[i], l)) % MOD;
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else ans = (ans + powmod(tot[i], l)) % MOD;
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}
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return (ans % MOD + MOD) % MOD;
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}
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void solve(){
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int ans = 0;
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for(int i = 1; i * i <= n; i ++) if(n % i == 0) {
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ans = (ans + (LL)cal(i) * phi[n / i]) % MOD;
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if(i * i != n)
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ans = (ans + (LL)cal(n / i) * phi[i]) % MOD;
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}
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printf("%d\n", (ans + MOD) % MOD / n);
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}
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int main(){
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init();
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scanf("%d", &cas);
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while (cas--) {
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scanf("%d%d", &m, &n);
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MOD = 10007 * n;
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memset(tot, 0, sizeof tot);
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maxm = 0;
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for (int i = 1; i <= m; i++) {
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scanf("%d", &tx);
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maxm = max(tx, maxm);
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for (int j = 0; j < facs[tx]; j++)
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tot[fac[tx][j]]++;
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}
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solve();
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}
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return 0;
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}
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