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 s[1000005];
int main() {
  int n, i, j, k, ans;
  while (cin >> n >> k >> s) {
    ans = 0;
    if (k == 2) {
      int a = 0, b = 0;
      for (i = 0; i < n; i++) {
        if (i % 2 == 0 && s[i] != 'A' || i % 2 == 1 && s[i] != 'B') ++a;
        if (i % 2 == 0 && s[i] != 'B' || i % 2 == 1 && s[i] != 'A') ++b;
      }
      if (a < b) {
        ans = a;
        for (i = 0; i < n; i++) {
          if (i % 2 == 0 && s[i] != 'A')
            s[i] = 'A';
          else if (i % 2 == 1 && s[i] != 'B')
            s[i] = 'B';
        }
      } else {
        ans = b;
        for (i = 0; i < n; i++) {
          if (i % 2 == 0 && s[i] != 'B')
            s[i] = 'B';
          else if (i % 2 == 1 && s[i] != 'A')
            s[i] = 'A';
        }
      }
    } else {
      for (i = 1; i < n; i++) {
        if (s[i] != s[i - 1]) continue;
        for (j = 0; j < k; j++)
          if (s[i] - 'A' != j && (i + 1 >= n || s[i + 1] - 'A' != j)) break;
        ++ans;
        s[i] = j + 'A';
      }
    }
    cout << ans << endl << s << endl;
  }
  return 0;
}