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 n, k, cnt, p;
string s, u, v;
int main() {
  scanf("%d%d", &n, &k);
  cin >> s;
  if (k == 2) {
    char ch;
    for (int i = 0; i < n; i++) {
      if ((i & 1)) {
        ch = 'B';
        u += ch;
        if (ch != s[i]) cnt++;
      } else {
        ch = 'A';
        u += ch;
        if (ch != s[i]) cnt++;
      }
    }
    p = cnt;
    cnt = 0;
    for (int i = 0; i < n; i++) {
      if ((i & 1)) {
        ch = 'A';
        v += ch;
        if (ch != s[i]) cnt++;
      } else {
        ch = 'B';
        v += ch;
        if (ch != s[i]) cnt++;
      }
    }
    (cnt < p) ? cout << cnt << "\n"
                     << v << endl
              : cout << p << "\n"
                     << u << endl;
  } else {
    cnt = 0;
    for (int i = 0; i < n; i++) {
      if (s[i] == s[i + 1]) {
        char ch = 'A';
        cnt++;
        while (ch == s[i] || ch == s[i + 2]) ch++;
        s[i + 1] = ch;
      }
    }
    cout << cnt << "\n" << s << endl;
  }
  return 0;
}