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>
int n, k;
int dp[500010][30], path[500010][30];
char s[500010];
int min(int a, int b) { return a < b ? a : b; }
void print(int n, int index) {
  if (n == 0) return;
  print(n - 1, path[n][index]);
  printf("%c", index + 'A' - 1);
}
int main() {
  while (2 == scanf("%d%d", &n, &k)) {
    scanf("%s", s + 1);
    memset(dp, -1, sizeof(dp));
    for (int i = 1; i <= k; i++) dp[1][i] = 1;
    dp[1][s[1] - 'A' + 1] = 0;
    for (int i = 2; i <= n; i++)
      for (int j = 1; j <= k; j++) {
        int tp = s[i] - 'A' + 1;
        if (tp == j) {
          for (int w = 1; w <= k; w++) {
            if (w == j) continue;
            if (dp[i][j] == -1 || dp[i][j] > dp[i - 1][w])
              dp[i][j] = dp[i - 1][w], path[i][j] = w;
          }
        } else {
          for (int w = 1; w <= k; w++) {
            if (w == j) continue;
            if (dp[i][j] == -1 || dp[i][j] > dp[i - 1][w] + 1)
              dp[i][j] = dp[i - 1][w] + 1, path[i][j] = w;
          }
        }
      }
    int index = 1;
    for (int i = 2; i <= k; i++) {
      if (dp[n][i] < dp[n][index]) index = i;
    }
    printf("%d\n", dp[n][index]);
    print(n, index);
    puts("");
  }
  return 0;
}