Minimum number of steps 805D

http://codeforces.com/contest/805/problem/D

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 modulo10⁹ + 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 from1 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：将字符串中ab 替换成 bba 进行多少次操作字符串中没有 ab

分析：将字符ab 替换成 bba 可以看成 a 向右移动一位, ab 中的 b 后增加一个 b

　　  每次将a 字符移动到所有b字符 的右端， 下一个a右边的b就多了一倍， 所以每遇到一个a 加上右边的b，然后更新右边的b为2*b

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

const ll mod = 1e9 + 7;
// "ab" ?→? "bba".
// "aab" ?→? "abba" ?→? "bbaba"?→? "bbbbaa".

int main(){
    string str;
    while(cin >> str){
        //cout << str << endl;
        ll b = 0;
        ll ans = 0;
        for(ll i = str.length() - 1; i >= 0; i--){
            // cout << "b " << b<< endl;
            if(str[i] == 'b')
                b++;
            //cout << "b " << b<< endl;
            if(str[i] == 'a'){
                ans += b%mod;
                //cout << ans << endl;
                ans %= mod;
                b *= 2;
                b %= mod;
            }
        }
        cout << ans% mod << endl;
    }
}