You are given a string S of length n with each character being one of the first m lowercase English letters. 

Calculate how many different strings T of length n composed from the first m lowercase English letters exist such that the length of LCS (longest common subsequence) between S and T is n - 1.

Recall that LCS of two strings S and T is the longest string C such that C both in S and T as a subsequence.


-----Input-----

The first line contains two numbers n and m denoting the length of string S and number of first English lowercase characters forming the character set for strings (1 ≤ n ≤ 100 000, 2 ≤ m ≤ 26).

The second line contains string S.


-----Output-----

Print the only line containing the answer.


-----Examples-----
Input
3 3
aaa

Output
6

Input
3 3
aab

Output
11

Input
1 2
a

Output
1

Input
10 9
abacadefgh

Output
789



-----Note-----

For the first sample, the 6 possible strings T are: aab, aac, aba, aca, baa, caa. 

For the second sample, the 11 possible strings T are: aaa, aac, aba, abb, abc, aca, acb, baa, bab, caa, cab.

For the third sample, the only possible string T is b.

Difficulty: competition

Starter code:

Solutions:
n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = map(int, input().split())
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)

n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = list(map(int, input().split()))
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)


n, m = map(int, input().split())
s = input()
p = c = 0
for i in range(1, n):
    if s[i] == s[i - 1]:
        c += n * (m - 1)
        p = i
    elif s[i] != s[i - 2]:
        p = i - 1
    c += i - p
ans = n * n * (m - 1) - c
print(ans)