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#include<cstdio>
using namespace std;
typedef long long LL;
//求组合数公式原始方法
//优点：从定义出发，易理解
//缺点：过早溢出，比如 C1(17,54)得到了负数
LL C1(int n, int m) {
if (m < n - m) m = n - m; //此处加了一个小优化，使用了公式2
LL ans = 1;
for (int i = m + 1; i <= n; i++) ans *= i;
for (int i = 1; i <= n - m; i++) ans /= i;
return ans;
}
//求组合数的优化后办法
//优点：从1开始除和乘，可以防止过早溢出和除法除不尽
LL C2(int n, int m) {
LL sum = 1;
for (int i = 1; i <= m; i++)
sum = sum * (n - m + i) / i;
return sum;
int main() {
printf("%lld\n", C1(54, 17));
printf("%lld\n", C2(54, 17));
return 0;
