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][26];
char color[500001];
int main() {
  int n, k;
  scanf("%d %d", &n, &k);
  scanf("%s", color);
  for (int i = 0; i < n; ++i) color[i] -= 'A';
  for (int i = n - 1; i >= 0; --i) {
    for (int j = 0; j < k; ++j) {
      dp[i][j] = 999999999;
      for (int z = 0; z < k; ++z) {
        if (j == z) continue;
        dp[i][j] = min(dp[i][j], dp[i + 1][z] + (j != color[i]));
      }
    }
  }
  int imin = 0;
  for (int i = 0; i < k; ++i) {
    if (dp[0][imin] > dp[0][i]) {
      imin = i;
    }
  }
  printf("%d\n", dp[0][imin]);
  for (int i = 0; i < n; ++i) {
    printf("%c", imin + 'A');
    for (int j = 0; j < k; ++j) {
      if (imin == j) continue;
      if (dp[i + 1][j] == dp[i][imin] - (imin != color[i])) {
        imin = j;
        break;
      }
    }
  }
  return 0;
}