codeforces 276D 贪心

妖狐艹你老母 2022-07-24 06:26 188阅读 0赞

D. Little Girl and Maximum XOR

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

A little girl loves problems on bitwise operations very much. Here's one of them.

You are given two integers *l* and *r*. Let's consider the values of ![32eb11ca3b3e1412a8a8cf28f1e899063f73cd50.png][] for all pairs of integers *a* and *b* (*l* ≤ *a* ≤ *b* ≤ *r*). Your task is to find the maximum value among all considered ones.

Expression ![6414d574a1ee8301d86f2c5d15396d8dc4328313.png][] means applying bitwise excluding or operation to integers *x* and *y*. The given operation exists in all modern programming languages, for example, in languages *C*\++ and *Java* it is represented as "^", in *Pascal* — as «xor».

Input

The single line contains space-separated integers *l* and *r* (1 ≤ *l* ≤ *r* ≤ 1018).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64dspecifier.

Output

In a single line print a single integer — the maximum value of ![32eb11ca3b3e1412a8a8cf28f1e899063f73cd50.png][] for all pairs of integers *a*, *b* (*l* ≤ *a* ≤ *b* ≤ *r*).

Examples

input

1 2

output

input

8 16

output

input

1 1

output

题意:  给定l和r, 求l-r之间的两个数x,y, 使得x^y有最大值.

分析: 贪心的思想, 从高位开始枚举, 当某一位l和r的二进制位不一样的时候, 那么这一位就肯定可以选到1, 让x这一位取1, y这一位取0, x后面的位全部取0,y后面的为全部取1, 两者异或就会出现二进制位上全部是1的最大值, 而且x跟y不会超范围, 这点举几个例子就看出来了.

#include<bits/stdc++.h>
    
    #define inf 0x3f3f3f3f
    using namespace std;
    
    typedef long long ll;
    typedef pair<int,int> pii;
    
    const int N=100010,MOD=1e9+7;
    
    
    int main()
    {
        ll a,b;
        cin>>a>>b;
        int i=61;
        for(;i>=0;i--)
        {
            if((a&(1LL<<i)) ^ (b&(1LL<<i))) break;
        }
        ll ans=0;
        for(;i>=0;i--) ans |= 1LL<<i;
        cout<<ans;
        return 0;
    }

[32eb11ca3b3e1412a8a8cf28f1e899063f73cd50.png]: /images/20220722/1235ffa0127542a6af3e22362b215dd7.png
[6414d574a1ee8301d86f2c5d15396d8dc4328313.png]: /images/20220722/e1c33d1299e240d6980a67ab789ed8e7.png