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2 years ago
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long LL;
const int maxn = 10000;
const LL Six = 166666668; /// 62关于mod的乘法逆元
const LL Two = 500000004;
const LL mod = 1e9 + 7; /// 尽量这样定义mod ,减少非必要的麻烦
bool book[maxn];
int pri[1300], cnt; /// 素数表
int factor[130]; /// 因子表
void Prime() {
memset(book, 0, sizeof(book));
cnt = 0;
book[0] = book[1] = 1;
for (int i = 2; i < maxn; i++) {
if (!book[i])
pri[cnt++] = i;
for (int j = 0; j < cnt && pri[j] * i < maxn; j++) {
book[i * pri[j]] = 1;
if (i % pri[j] == 0)
break;
}
}
}
inline LL Mod(LL a, LL b) {
return (a % mod) * (b % mod) % mod;
}
inline LL F(LL k, LL n) { /// 求(k*n)^2+k*n
return (Mod(k, k) * Mod(Mod(n, n + 1), Mod(n + n + 1, Six)) % mod + Mod(Mod(1 + n, n), Mod(k, Two))) % mod;
}
int main() {
LL n, m;
Prime();
while (~scanf("%lld%lld", &n, &m)) {
int fac_cnt = 0; /// 素数因子的个数
for (int i = 0; i < cnt; i++) {
if (pri[i] > m) break;
if (m % pri[i] == 0) {
factor[fac_cnt++] = pri[i];
while (m % pri[i] == 0) m /= pri[i];
}
}
if (m > 1) factor[fac_cnt++] = m;
LL sum = F(1LL, n), ans = 0; /// 计算总和sum
LL item = 1 << fac_cnt; /// 开始容斥
/// 例如有3个因子那么item=1<<3=8(1000二进制)
/// 然后i从1开始枚举直到7(111二进制i中二进制的位置1表式取这个位置的因子
/// 例如i=3(11二进制) 表示去前两个因子i=5101表示取第1个和第3个的因子
for (int i = 1; i < item; i++) {
int num = 0, x = 1;
for (int j = 0; j < fac_cnt; j++) {
if (1 & (i >> j)) num++, x *= factor[j];
}
if (num & 1)
ans = (ans + F(x, n / x)) % mod; /// 根据容斥,取奇数个因子时,应加上
else
ans = ((ans - F(x, n / x)) % mod + mod) % mod;
}
printf("%lld\n", ((sum - ans) % mod + mod) % mod);
}
return 0;
}