Tavas is a strange creature. Usually "zzz" comes out of people's mouth while sleeping, but string s of length n comes out from Tavas' mouth instead. [Image] 

Today Tavas fell asleep in Malekas' place. While he was sleeping, Malekas did a little process on s. Malekas has a favorite string p. He determined all positions x_1 < x_2 < ... < x_{k} where p matches s. More formally, for each x_{i} (1 ≤ i ≤ k) he condition s_{x}_{i}s_{x}_{i} + 1... s_{x}_{i} + |p| - 1 = p is fullfilled.

Then Malekas wrote down one of subsequences of x_1, x_2, ... x_{k} (possibly, he didn't write anything) on a piece of paper. Here a sequence b is a subsequence of sequence a if and only if we can turn a into b by removing some of its elements (maybe no one of them or all).

After Tavas woke up, Malekas told him everything. He couldn't remember string s, but he knew that both p and s only contains lowercase English letters and also he had the subsequence he had written on that piece of paper.

Tavas wonders, what is the number of possible values of s? He asked SaDDas, but he wasn't smart enough to solve this. So, Tavas asked you to calculate this number for him.

Answer can be very large, so Tavas wants you to print the answer modulo 10^9 + 7.


-----Input-----

The first line contains two integers n and m, the length of s and the length of the subsequence Malekas wrote down (1 ≤ n ≤ 10^6 and 0 ≤ m ≤ n - |p| + 1).

The second line contains string p (1 ≤ |p| ≤ n).

The next line contains m space separated integers y_1, y_2, ..., y_{m}, Malekas' subsequence (1 ≤ y_1 < y_2 < ... < y_{m} ≤ n - |p| + 1).


-----Output-----

In a single line print the answer modulo 1000 000 007.


-----Examples-----
Input
6 2
ioi
1 3

Output
26

Input
5 2
ioi
1 2

Output
0



-----Note-----

In the first sample test all strings of form "ioioi?" where the question mark replaces arbitrary English letter satisfy.

Here |x| denotes the length of string x.

Please note that it's possible that there is no such string (answer is 0).

Difficulty: interview

Starter code:

Solutions:
# -*- coding: utf-8 -*-


def solve():
    mod = 10**9 + 7
    n, m = map(int, input().split())
    p = input()
    if m == 0:
        return powmod(n)
    delta = len(p) - 1
    ys = map(int, input().split())
    answer = 1
    tail = 0
    for y in ys:
        if y > tail:
            answer *= powmod(y - tail - 1)
            answer %= mod
        elif not is_consistent(p, tail - y + 1):
            return 0
        tail = y + delta
    answer *= powmod(n - tail)
    return answer % mod

ok_set = set()
def is_consistent(p, margin):
    nonlocal ok_set
    if margin in ok_set:
        return True
    elif p[:margin] == p[-margin:]:
        ok_set.add(margin)
        return True
    else:
        return False

def powmod(p):
    mod = 10**9 + 7
    pbin = bin(p)[2:][-1::-1]
    result = 26 if pbin[0] == '1' else 1
    tmp = 26
    for bit in pbin[1:]:
        tmp *= tmp
        tmp %= mod
        if bit == '1':
            result *= tmp
            result %= mod
    return result

print(solve())

# -*- coding: utf-8 -*-


def solve():
    n, m = list(map(int, input().split()))
    p = input()
    if m == 0:
        return powmod(n)
    delta = len(p) - 1
    ys = list(map(int, input().split()))
    tail = 0
    free_chars = 0
    for y in ys:
        if y > tail:
            free_chars += y - tail - 1
        elif not is_consistent(p, tail - y + 1):
            return 0
        tail = y + delta
    free_chars += n - tail
    return powmod(free_chars)

ok_set = set()
def is_consistent(p, margin):
    nonlocal ok_set
    if margin in ok_set:
        return True
    elif p[:margin] == p[-margin:]:
        ok_set.add(margin)
        return True
    else:
        return False


def powmod(p):
    mod = 10**9 + 7
    pbin = bin(p)[2:][-1::-1]
    result = 26 if pbin[0] == '1' else 1
    tmp = 26
    for bit in pbin[1:]:
        tmp *= tmp
        tmp %= mod
        if bit == '1':
            result *= tmp
            result %= mod
    return result


print(solve())


import sys

def prefix(s):
    m = len(s)
    v = [0]*len(s)
    for i in range(1,len(s)):
        k = v[i-1]
        while k > 0 and s[k] != s[i]:
            k = v[k-1]
        if s[k] == s[i]:
            k = k + 1
        v[i] = k
    w = set()
    i = m-1
    while v[i] != 0:
        w.add(m-v[i])
        i = v[i]-1
    
    return w
n,m = list(map(int, input().split()))
if m == 0: 
    print(pow(26, n, 1000000007))
    return
p = input()
l = len(p)
x = list(map(int,input().split()))
w = prefix(p)
busy = l
for i in range(1,m):
    if x[i]-x[i-1] < l and (x[i] - x[i-1]) not in w:
        print(0)
        return
    busy += min(x[i]-x[i-1], l)
    
print(pow(26,n-busy, 1000000007))