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 a, b, c, d, ans, ans1, ans2;
string s;
int main() {
  cin >> a >> b;
  cin >> s;
  if (b != 2) {
    for (int i = 1; i <= a - 2; i++) {
      if (s[i] == s[i - 1]) {
        if (s[i - 1] != 'A' && s[i + 1] != 'A') s[i] = 'A';
        if (s[i - 1] != 'B' && s[i + 1] != 'B') s[i] = 'B';
        if (s[i - 1] != 'C' && s[i + 1] != 'C') s[i] = 'C';
        ans++;
      }
    }
    if (s[a - 1] == s[a - 2]) {
      if (s[a - 2] != 'A') s[a - 1] = 'A';
      if (s[a - 2] != 'B') s[a - 1] = 'B';
      if (s[a - 2] != 'C') s[a - 1] = 'C';
      ans++;
    }
    cout << ans << endl << s;
    return 0;
  }
  for (int i = 0; i <= a - 1; i++) {
    if (i % 2 == 0 && s[i] != 'A') {
      ans1++;
    }
    if (i % 2 == 1 && s[i] != 'B') {
      ans1++;
    }
    if (i % 2 == 0 && s[i] != 'B') {
      ans2++;
    }
    if (i % 2 == 1 && s[i] != 'A') {
      ans2++;
    }
  }
  if (ans1 < ans2) {
    cout << ans1 << endl;
    for (int i = 1; i <= a; i++) {
      if (i % 2 == 0)
        cout << 'B';
      else
        cout << 'A';
    }
  } else {
    cout << ans2 << endl;
    for (int i = 1; i <= a; i++) {
      if (i % 2 == 0)
        cout << 'A';
      else
        cout << 'B';
    }
  }
}