Minimum number of steps CodeForces

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

Copy

ab

output

Copy

1

input

Copy

aab

output

Copy

3

Note

The first example: "ab"  →  "bba".

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

从后向前 遍历

每个a都会把它后边的b变到后边 且乘二  

而每个a后边b的个数 即为当前a变化的次数

#include <bits/stdc++.h>
#define mem(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long LL;
const int maxn = 1000010, INF = 0x7fffffff;
const int MOD = 1e9 + 7;
int n;
string str;


int main()
{

    cin >> str;
    int len = str.size();
    int ans = 0, cnt = 0;
    for(int i = len - 1; i >= 0; i--)
    {
        if(str[i] == 'b')
            cnt++;
        else
        {
            ans = (ans + cnt) % MOD;
            cnt = (cnt * 2) % MOD;
        }

    }
    cout << ans << endl;




    return 0;
}

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

Copy

ab

output

Copy

1

input

Copy

aab

output

Copy

3

Note

The first example: "ab"  →  "bba".

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