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 main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  int ans = 0, len, k, i, d1 = 0, d2 = 0;
  string s;
  string temp;
  string t2;
  cin >> len >> k;
  cin >> s;
  if (k == 2) {
    for (i = 0; i < len; i++) {
      if (i % 2)
        temp.push_back('A');
      else
        temp.push_back('B');
      if (temp[i] != s[i]) d1++;
    }
    for (i = 0; i < len; i++) {
      if (i % 2)
        t2.push_back('B');
      else
        t2.push_back('A');
      if (t2[i] != s[i]) d2++;
    }
    if (d1 < d2)
      cout << d1 << "\n" << temp << "\n";
    else
      cout << d2 << "\n" << t2 << "\n";
  } else {
    for (i = 1; i < (len - 1); i++) {
      if (s[i] == s[i - 1]) {
        ans++;
        if ('A' != s[i] && 'A' != s[i + 1])
          s[i] = 'A';
        else if ('C' != s[i] && 'C' != s[i + 1])
          s[i] = 'C';
        else if ('B' != s[i] && 'B' != s[i + 1])
          s[i] = 'B';
      }
    }
    if (len >= 2) {
      if (s[len - 1] == s[len - 2]) {
        ans++;
        if ('A' != s[len - 1])
          s[len - 1] = 'A';
        else
          s[len - 1] = 'B';
      }
    }
    cout << ans << "\n" << s << "\n";
  }
  return 0;
}