CF-805D

D. Minimum number of steps

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

We have a string of letters 'a' and 'b'. We want to perform some operations on it. On each step we choose one of substrings "ab" in the string and replace it with the string "bba". If we have no "ab" as a substring, our job is done. Print the minimum number of steps we should perform to make our job done modulo 109 + 7.

The string "ab" appears as a substring if there is a letter 'b' right after the letter 'a' somewhere in the string.

Input

The first line contains the initial string consisting of letters 'a' and 'b' only with length from 1 to 106.

Output

Print the minimum number of steps modulo 109 + 7.

Examples

input

ab

output

1

input

aab

output

3

Note

The first example: "ab"  →  "bba".

The second example: "aab"  →  "abba"  →  "bbaba"  →  "bbbbaa".

题意：

对于给定字符串，我们可将其中的子串“ab”替换成“bba”，直到没有子串“ab”。

求操作次数。

由题意可知，a后的一个b会变成a前的两个b。

我们可以反向遍历，记录b的个数，每遇到a做一次操作。b*=2.继续。

附AC代码：

#include<bits/stdc++.h>
using namespace std;

const int mod=1e9+7;

int main(){
    string s;
    cin>>s;
    long long ans=0,cnt=0;
    int n=s.size();
    for(int i=n-1;i>=0;i--){
        if(s[i]=='b')
        cnt++;
        else{
            ans+=cnt;
            ans%=mod;
            cnt=cnt*2%mod;
        }
    }
    cout<<ans%mod<<endl;
    return 0;
}