diff --git a/TangDou/Topic/SpareTire.cpp b/TangDou/Topic/SpareTire.cpp index 4ee8081..1d3e39e 100644 --- a/TangDou/Topic/SpareTire.cpp +++ b/TangDou/Topic/SpareTire.cpp @@ -25,17 +25,18 @@ signed main() { #endif int n, m; - int rev6 = qmi(6, mod - 2); - int rev2 = qmi(2, mod - 2); + int Six = qmi(6, mod - 2); // 因为需要用到 % 1e9+7 下6的逆元,用费马小定理+快速幂求逆元 + int Two = qmi(2, mod - 2); // 因为需要用到 % 1e9+7 下2的逆元,用费马小定理+快速幂求逆元 while (cin >> n >> m) { - int res = n * (n + 1) % mod * (2 * n + 1) % mod * rev6 % mod; - int t = n * (n + 1) % mod * rev2 % mod; + // 所结果拆分为平方和公式,等差数列两部分 + // 注意:现在求的是整体值,还没有去掉不符合条件的数字 + int first = n * (n + 1) % mod * (2 * n + 1) % mod * Six % mod; + int second = n * (n + 1) % mod * Two % mod; + int res = (first + second) % mod; - res = (res + t) % mod; - - // 质因子分解 - t = m; // 复制出来 + // 对m进行质因子分解 + int t = m; // 复制出来 for (int i = 2; i * i <= t; i++) { if (t % i == 0) { p.push_back(i); @@ -51,17 +52,18 @@ signed main() { 例如i=3(11二进制) 表示取前两个因子,i=5(101)表示取第1个和第3个的因子 */ for (int i = 1; i < (1 << p.size()); i++) { - int cnt = 0, tmp = 1; + int cnt = 0, s = 1; for (int j = 0; j < p.size(); j++) if ((i >> j) & 1) { cnt++; - tmp *= p[j]; + s *= p[j]; } - int nn = n / tmp; - int pt = (nn) % mod * (nn + 1) % mod * (2 * nn + 1) % mod * rev6 % mod; - pt = pt * tmp % mod * tmp % mod; - pt = (pt + nn * (tmp + tmp * nn) % mod * rev2 % mod) % mod; + int nn = n / s; + int pt = (nn) % mod * (nn + 1) % mod * (2 * nn + 1) % mod * Six % mod; + pt = pt * s % mod * s % mod; + pt = (pt + nn * (s + s * nn) % mod * Two % mod) % mod; + if (cnt & 1) res = (res - pt + mod) % mod; else