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Score : $600$ points

Problem Statement

There is a length $L$ string $S$ consisting of uppercase and lowercase English letters displayed on an electronic bulletin board with a width of $W$. The string $S$ scrolls from right to left by a width of one character at a time.

The display repeats a cycle of $L+W-1$ states, with the first character of $S$ appearing from the right edge when the last character of $S$ disappears from the left edge.

For example, when $W=5$ and $S=$ ABC, the board displays the following seven states in a loop:

• ABC..
• BC...
• C....
• ....A
• ...AB
• ..ABC
• .ABC.

(. represents a position where no character is displayed.)

More precisely, there are distinct states for $k=0,\ldots,L+W-2$ in which the display is as follows.

• Let $f(x)$ be the remainder when $x$ is divided by $L+W-1$. The $(i+1)$-th position from the left of the board displays the $(f(i+k)+1)$-th character of $S$ when $f(i+k)<L$, and nothing otherwise.

You are given a length $W$ string $P$ consisting of uppercase English letters, lowercase English letters, ., and _.
Find the number of states among the $L+W-1$ states of the board that coincide $P$ except for the positions with _.
More precisely, find the number of states that satisfy the following condition.

• For every $i=1,\ldots,W$, one of the following holds.
  • The $i$-th character of $P$ is _.
  • The character displayed at the $i$-th position from the left of the board is equal to the $i$-th character of $P$.
  • Nothing is displayed at the $i$-th position from the left of the board, and the $i$-th character of $P$ is ..

Constraints

• $1 \leq L \leq W \leq 3\times 10^5$
• $L$ and $W$ are integers.
• $S$ is a string of length $L$ consisting of uppercase and lowercase English letters.
• $P$ is a string of length $W$ consisting of uppercase and lowercase English letters, ., and _.

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Input

The input is given from Standard Input in the following format:

$L$ $W$

$S$

$P$

Output

Print the answer.

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3 5
ABC
..___

3

There are three desired states, where the board displays ....A, ...AB, ..ABC.

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11 15
abracadabra
__.._________ab

2

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20 30
abaababbbabaabababba
__a____b_____a________________

2

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1 1
a
_

1