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;
char row[500005];
char ans[500005];
int dp[500005][26];
int main() {
  int n, K;
  scanf("%d%d", &n, &K);
  scanf("%s", row);
  for (int i = 0; i <= n; ++i) {
    for (int j = 0; j < K; ++j) {
      dp[i][j] = INT_MAX;
    }
  }
  for (int i = 0; i < 26; ++i) {
    dp[0][i] = 0;
  }
  for (int i = 1; i <= n; ++i) {
    for (int j = 0; j < K; ++j) {
      for (int k = 0; k < K; ++k) {
        if (j == k) continue;
        if (j == row[i - 1] - 'A') {
          dp[i][j] = min(dp[i][j], dp[i - 1][k]);
        } else {
          dp[i][j] = min(dp[i][j], dp[i - 1][k] + 1);
        }
      }
    }
  }
  int mins = INT_MAX, f = -1;
  for (int i = 0; i < K; ++i) {
    if (dp[n][i] < mins) {
      mins = dp[n][i];
      f = i;
    }
  }
  for (int i = n - 1; i > 0; --i) {
    ans[i] = f + 'A';
    for (int j = 0; j < K; ++j) {
      if (j == f) continue;
      if ((row[i] != f + 'A' && dp[i + 1][f] == dp[i][j] + 1) ||
          (row[i] == f + 'A' && dp[i + 1][f] == dp[i][j])) {
        f = j;
        break;
      }
    }
  }
  ans[0] = f + 'A';
  ans[n] = '\0';
  printf("%d\n", mins);
  printf("%s\n", ans);
  return 0;
}