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() {
  int n, k;
  string s;
  cin >> n >> k >> s;
  if (n == 1) {
    cout << 0 << endl << s;
    return 0;
  } else if (n == 2) {
    if (s[0] == s[1]) {
      cout << 1 << endl;
      cout << s[0] << char((s[1] - 'A' + 1) % k + 'A');
    } else
      cout << 0 << endl << s;
    return 0;
  }
  if (k == 2) {
    string s1(n, 'A'), s2(n, 'B');
    for (int i = 0; i < n; i++) {
      if (i & 1) {
        s1[i] = 'B';
        s2[i] = 'A';
      }
    }
    int ans1 = 0, ans2 = 0;
    for (int i = 0; i < n; i++)
      if (s[i] != s1[i]) ans1++;
    for (int i = 0; i < n; i++)
      if (s[i] != s2[i]) ans2++;
    if (ans1 < ans2)
      cout << ans1 << endl << s1;
    else
      cout << ans2 << endl << s2;
  } else {
    int ans = 0;
    for (int i = 1; i < n - 1; i++)
      if (s[i] == s[i - 1] and s[i] == s[i + 1]) {
        s[i] = char('A' + (s[i] - 'A' + 1) % k);
        ans++;
      }
    for (int i = 1; i < n - 1; i++) {
      bool aux = false;
      while (s[i] == s[i - 1] or s[i] == s[i + 1]) {
        aux = true;
        s[i] = char('A' + (s[i] - 'A' + 1) % k);
      }
      if (aux) ans++;
    }
    cout << ans << endl << s;
  }
  return 0;
}