The Fair Nut and String

1000ms

262144K

Description:

The Fair Nut found a string $$$s$$$. The string consists of lowercase Latin letters. The Nut is a curious guy, so he wants to find the number of strictly increasing sequences $$$p_1, p_2, \ldots, p_k$$$, such that:

For each $$$i$$$ ($$$1 \leq i \leq k$$$), $$$s_{p_i} =$$$ 'a'.
For each $$$i$$$ ($$$1 \leq i < k$$$), there is such $$$j$$$ that $$$p_i < j < p_{i + 1}$$$ and $$$s_j =$$$ 'b'.

The Nut is upset because he doesn't know how to find the number. Help him.

This number should be calculated modulo $$$10^9 + 7$$$.

Input:

The first line contains the string $$$s$$$ ($$$1 \leq |s| \leq 10^5$$$) consisting of lowercase Latin letters.

Output:

In a single line print the answer to the problem — the number of such sequences $$$p_1, p_2, \ldots, p_k$$$ modulo $$$10^9 + 7$$$.

Sample Input:

abbaa

Sample Output:

Sample Input:

baaaa

Sample Output:

Sample Input:

agaa

Sample Output:

Note:

In the first example, there are $$$5$$$ possible sequences. $$$[1]$$$, $$$[4]$$$, $$$[5]$$$, $$$[1, 4]$$$, $$$[1, 5]$$$.

In the second example, there are $$$4$$$ possible sequences. $$$[2]$$$, $$$[3]$$$, $$$[4]$$$, $$$[5]$$$.

In the third example, there are $$$3$$$ possible sequences. $$$[1]$$$, $$$[3]$$$, $$$[4]$$$.

Informação

Provedor Codeforces

Código CF1084C