UVA 11440 Help Tomisu 欧拉函数 数论

非常好的数论题 结合了很多不知道的知识点

 易得代码

#include<iostream>
#include<unordered_map>
#include<algorithm>
#include<string>
#include<cmath>
#include<cstring>
#include<vector>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<sstream>
#include<cstdio>
#define INF 0x3f3f3f3f
#define eps 1e-8
#define equals(a,b) (fabs(a-b)<eps)
#define MOD 100000007
const int maxn = 1e7+5 ;
const double PI = acos(-1.0);
typedef long long ll;
using namespace std;

int prime[maxn + 5];
int is_prime[maxn + 5];
int cnt;
ll fac[maxn];
ll phi[maxn];
ll n, m;

ll exgcd(ll a, ll b, ll& x, ll& y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }

    ll g = exgcd(b, a % b, x, y);
    ll t = x;
    x = y;
    y = t - a / b * y;
    return g;
}


ll inv(ll a, ll n) {
    ll x, y;
    exgcd(a, n, x, y);
    return (x + n) % n;
}

void is_Prime() {
    is_prime[0] = is_prime[1] = 1;
    for (int i = 2; i <= maxn; i++) {
        if (!is_prime[i]) {
            prime[cnt++] = i;
            for (int j = 2 * i; j <= maxn; j += i) {
                is_prime[j] = 1;
            }
        }
    }
}

void phi_table() {
    fac[0] = fac[1] = 1;
    phi[0] = phi[1] = 1;
    for (ll i = 2; i < maxn - 3; i++) {
        fac[i] = (fac[i - 1] * i) % MOD;
        if (is_prime[i]) {
            phi[i] = phi[i - 1];
            continue;
        }
        phi[i] = phi[i - 1] * (i - 1) % MOD * inv(i, MOD) % MOD;
    }
}

int main() {
    ll ans;
    is_Prime();
    phi_table();
    while (scanf("%lld%lld", &n, &m), n && m) {
        printf("%lld\n", ((fac[n] * phi[m] - 1) % MOD + MOD) % MOD);
    }

    return 0;
}