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;
const int N = 5e5 + 10;
int main() {
  int n, k;
  cin >> n >> k;
  string s;
  int ans = 0;
  cin >> s;
  if (k == 2) {
    string tmp, tmp2;
    int cur = 0;
    int tval = 0;
    for (int i = 0; i < n; ++i) {
      if (cur) {
        tmp.push_back('A');
        cur ^= 1;
        if (s[i] != 'A') ans++;
      } else {
        tmp.push_back('B');
        cur ^= 1;
        if (s[i] != 'B') ans++;
      }
    }
    cur = 0;
    for (int i = 0; i < n; ++i) {
      if (cur) {
        tmp2.push_back('B');
        cur ^= 1;
        if (s[i] != 'B') tval++;
      } else {
        tmp2.push_back('A');
        cur ^= 1;
        if (s[i] != 'A') tval++;
      }
    }
    if (ans < tval) {
      cout << ans << '\n';
      cout << tmp << '\n';
      return 0;
    }
    cout << tval << '\n';
    cout << tmp2 << '\n';
    return 0;
  }
  for (int i = 1; i < n; ++i) {
    int j = i;
    while (s[j] == s[j - 1]) j++;
    int len = j - i + 1;
    char tofill = 'A';
    if (s[i] == 'A') tofill++;
    if (j != n && s[j] == tofill) tofill++;
    if (s[i] == tofill) tofill++;
    for (int k = i; k < j; k += 2) {
      ans++;
      s[k] = tofill;
    }
    i = j;
  }
  cout << ans << '\n';
  cout << s << '\n';
}