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 n, k, dp[600005][30], DP[600005][3], f[600000];
char s[600000];
int main() {
  memset(DP, -1, sizeof(DP));
  scanf("%d%d", &n, &k);
  scanf("%s", s);
  for (int i = 0; i < n; i++) f[i + 1] = s[i] - 'A' + 1;
  for (int i = 1; i <= n; i++) {
    for (int q = 1; q <= k; q++) {
      if (dp[i - 1][q] == DP[i - 1][1])
        dp[i][q] = DP[i - 1][2];
      else
        dp[i][q] = DP[i - 1][1];
      if (dp[i][q] == -1) dp[i][q]++;
      if (f[i] != q) dp[i][q]++;
      if (DP[i][1] == -1 || DP[i][1] > dp[i][q]) {
        DP[i][2] = DP[i][1];
        DP[i][1] = dp[i][q];
      } else {
        if (DP[i][2] == -1 || DP[i][2] > dp[i][q]) DP[i][2] = dp[i][q];
      }
    }
  }
  int Y = n;
  while (n > 0) {
    int mn = 600000;
    for (int i = 1; i <= k; i++) {
      if (dp[n][i] < mn && i != f[n + 1]) {
        mn = dp[n][i];
        f[n] = i;
      }
    }
    n--;
  }
  printf("%d\n", DP[Y][1]);
  for (int i = 1; i <= Y; i++) printf("%c", f[i] + 'A' - 1);
  return 0;
}