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() {
  long long n, k;
  string s;
  cin >> n >> k;
  cin >> s;
  int count;
  if (k > 2) {
    count = 0;
    for (int i = 1; i < s.size(); i++) {
      if (s[i] == s[i - 1]) {
        char a = 'A';
        bool cond1 = true;
        cond1 = a != s[i - 1];
        bool cond2 = true;
        if (i + 1 < s.size()) cond2 = a != s[i + 1];
        bool cond = cond1 && cond2;
        while (!cond) {
          a++;
          cond1 = true;
          if (i - 1 >= 0) cond1 = a != s[i - 1];
          cond2 = true;
          if (i + 1 < s.size()) cond2 = a != s[i + 1];
          cond = cond1 && cond2;
        }
        count++;
        s[i] = a;
      }
    }
  } else {
    int count1 = 0;
    int count2 = 0;
    string s2, s3;
    s2 = s;
    s3 = s;
    for (int i = 0; i < n; i++) {
      if (i % 2 == 0) {
        if (s2[i] == 'A') {
          count1++;
          s2[i] = 'B';
        }
      } else {
        if (s2[i] == 'B') {
          count1++;
          s2[i] = 'A';
        }
      }
    }
    for (int i = 0; i < n; i++) {
      if (i % 2 != 0) {
        if (s3[i] == 'A') {
          count2++;
          s3[i] = 'B';
        }
      } else {
        if (s3[i] == 'B') {
          count2++;
          s3[i] = 'A';
        }
      }
    }
    if (count1 < count2) {
      s = s2;
      count = count1;
    } else {
      s = s3;
      count = count2;
    }
  }
  cout << count << endl;
  cout << s << endl;
  return 0;
}