CodeForces804B

B. 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：将所有的a移动到b的后面，每走一步，一个ab变成bba，增加了一个b，问到无法移动的时候，一共移动了多少步。

思路：简单递推，从后往前处理，每次经过一个a，都要将它移到最后，共经过x个b，将ans+=x，同时b的个数翻倍x += x；每经过一个b，x++。

import java.util.*;public class Main {public static final long mod = 1000000000+7;public static void main(String[] args) {// TODO Auto-generated method stubScanner cin = new Scanner(System.in);String s = cin.next();long ans = 0;long num = 0;for(int i = s.length()-1;i>=0;i--){if(s.charAt(i) == 'a'){ans = (ans+num)%mod;num = (num+num)%mod;}else{num = (num + 1)%mod;}}System.out.println(ans);}}