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 dp[500001][30];
int data[500001];
char p[500001], ans[500001];
int pre[500001][30];
int k;
int main() {
  int i, len, j, a, m, now, num;
  while (~scanf("%d %d", &len, &k)) {
    num = 0;
    memset(pre, -1, sizeof(pre));
    scanf("%s", p);
    for (i = 0; i < len; i++) data[i] = p[i] - 'A';
    for (i = 0; i < 26; i++) dp[0][i] = 1;
    dp[0][data[0]] = 0;
    for (i = 1; i < len; i++) {
      for (j = 0; j < k; j++) {
        a = 1000000000;
        for (m = 0; m < k; m++) {
          if (j != m && dp[i - 1][m] < a) {
            a = dp[i - 1][m];
            now = m;
          }
        }
        pre[num + 1][j] = now;
        if (j == data[i])
          dp[i][j] = a;
        else
          dp[i][j] = a + 1;
      }
      num++;
    }
    a = 1000000000;
    for (i = 0; i < k; i++)
      if (a > dp[len - 1][i]) {
        now = i;
        a = dp[len - 1][i];
      }
    printf("%d\n", a);
    int t = 0;
    while (1) {
      ans[len - t - 1] = now + 'A';
      now = pre[num][now];
      num--;
      if (num == -1) break;
      t++;
    }
    ans[len] = '\0';
    puts(ans);
  }
  return 0;
}