Problem: A colored stripe is represented by a horizontal row of n square cells, each cell is pained one of k colors. Your task is to repaint the minimum number of cells so that no two neighbouring cells are of the same color. You can use any color from 1 to k to repaint the cells.

Input

The first input line contains two integers n and k (1 ≤ n ≤ 5·105; 2 ≤ k ≤ 26). The second line contains n uppercase English letters. Letter "A" stands for the first color, letter "B" stands for the second color and so on. The first k English letters may be used. Each letter represents the color of the corresponding cell of the stripe.

Output

Print a single integer — the required minimum number of repaintings. In the second line print any possible variant of the repainted stripe.

Examples

Input

6 3
ABBACC


Output

2
ABCACA


Input

3 2
BBB


Output

1
BAB

Solution (in PYTHON3):

Solution:

if __name__ == '__main__':
    n, k = [int(x) for x in input().split()]
    s = input()

    if(k == 2):
        str1 = "AB"*n
        str2 = "BA"*n
        diff1 = 0
        diff2 = 0
        for i in range(n):
            #str1 += chr(ord('A') + i%2)
            #str2 += chr(ord('B') - i%2)
            if(s[i] != str1[i]):
                diff1 += 1
            else:
                diff2 += 1
        if(diff1 < diff2):
            print(diff1)
            print(str1[:n])
        else:
            print(diff2)
            print(str2[:n])
    else:
        l = [chr(i + ord('A')) for i in range(k)]
        s += "_"
        s = "_" + s
        s = list(s)
        resVal = 0
        for i in range(1,n+1):
            if(s[i] != s[i-1]):
                continue
            resVal += 1
            possible_changes = [x for x in l if x != s[i-1] and x != s[i+1]]
            s[i] = possible_changes[0]

        del s[0]
        del s[-1]
        s = ''.join(s)
        print(resVal)
        print(s)