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题目链接:[[https://projecteuler.net/problem=207]]
=== 题意 ===
定义$4^t=2^t+k$是$k$的一个**拆分**，当且仅当$4^t,2^t,k$都是正整数，且$t$是实数。特别的当，$t$也是正整数时，称为**完美拆分**。定义函数$P(m)$为$1\lt k \le m$中完美拆分占所有拆分的比例
=== 题解 ===
拆分的式子可以化简为$2^t(2^t-1)=k$，不妨设$u=2^t$其中$u$是正整数，那么完美拆分显然就是$u$是$2$的整数次幂的情况，所以二分一下即可（应该是有单调性的吧
另外，直接枚举$2^t$中的$t$也是可以的
=== 代码 ===
#include
#define ll long long
#define pii_ pair
#define mp_ make_pair
#define pb push_back
#define fi first
#define se second
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define show1(a) cout<<#a<<" = "<