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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int F[500005][30], Path[500005][30];
char str[500005], Ctr[500005];
int main() {
  int i, j, t, n, k, ans;
  scanf("%d%d%s", &n, &k, str);
  memset(F, 0x0f, sizeof(F));
  F[0][1] = F[0][2] = 0;
  for (i = 1; i <= n; i++)
    for (j = 1; j <= k; j++) {
      for (t = 1; t <= k; t++)
        if (t != j) {
          if (F[i][j] > F[i - 1][t] + 1 - (j == str[i - 1] - 64))
            F[i][j] = F[i - 1][t] + 1 - (j == str[i - 1] - 64), Path[i][j] = t;
        }
    }
  for (ans = 0x0f0f0f0f, j = 1; j <= k; j++)
    if (ans > F[n][j]) ans = F[n][j], i = j;
  printf("%d\n", ans);
  for (t = i, j = n; j; t = Path[j][t], j--) Ctr[j - 1] = t + 64;
  Ctr[n] = '\0';
  printf("%s\n", Ctr);
  return 0;
}