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 l, k;
  cin >> l >> k;
  string s;
  cin >> s;
  s += '#';
  char a = 'A', b = 'B', c = 'C';
  string s1, s2;
  for (int i = 0; i < l; i++) {
    if (i % 2 == 0) {
      s1 += a;
      s2 += b;
    } else {
      s1 += b;
      s2 += a;
    }
  }
  if (k == 2) {
    int count1 = 0, count2 = 0;
    for (int i = 0; i < l; i++) {
      if (s[i] != s1[i]) count1++;
      if (s[i] != s2[i]) count2++;
    }
    if (count1 >= count2) {
      cout << count2 << endl;
      cout << s2 << endl;
    } else {
      cout << count1 << endl;
      cout << s1 << endl;
    }
    return 0;
  }
  int count = 0;
  string ans;
  int index = 0;
  ans += s[0];
  for (int i = 1; i < l; i++) {
    if (s[i] != s[i - 1])
      ans += s[i];
    else {
      if (s[i - 1] == a) {
        if (s[i + 1] == b) {
          s[i] = c;
          ans += c;
        } else if (s[i + 1] == c) {
          s[i] = b;
          ans += b;
        } else if (s[i + 1] == a) {
          s[i] = b;
          ans += b;
        } else {
          s[i] = b;
          ans += b;
        }
      } else if (s[i - 1] == b) {
        if (s[i + 1] == b) {
          ans += a;
          s[i] = a;
        } else if (s[i + 1] == c) {
          s[i] = a;
          ans += a;
        } else if (s[i + 1] == a) {
          s[i] = c;
          ans += c;
        } else {
          s[i] = a;
          ans += a;
        }
      } else if (s[i - 1] == c) {
        if (s[i + 1] == b) {
          s[i] = a;
          ans += a;
        } else if (s[i + 1] == c) {
          s[i] = a;
          ans += a;
        } else if (s[i + 1] == a) {
          s[i] = b;
          ans += b;
        } else {
          s[i] = a;
          ans += a;
        }
      } else if (s[i + 1] == a) {
        if (s[i - 1] == b) {
          s[i] = c;
          ans += c;
        } else if (s[i - 1] == c) {
          s[i] = b;
          ans += b;
        } else if (s[i - 1] == a) {
          s[i] = b;
          ans += b;
        } else {
          s[i] = b;
          ans += b;
        }
      } else if (s[i + 1] == b) {
        if (s[i - 1] == b) {
          s[i] = a;
          ans += a;
        } else if (s[i - 1] == c) {
          s[i] = a;
          ans += a;
        } else if (s[i - 1] == a) {
          s[i] = c;
          ans += c;
        } else {
          s[i] = a;
          ans += a;
        }
      } else if (s[i + 1] == c) {
        if (s[i - 1] == b) {
          s[i] = a;
          ans += a;
        } else if (s[i - 1] == c) {
          s[i] = a;
          ans += a;
        } else if (s[i - 1] == a) {
          s[i] = b;
          ans += b;
        } else {
          s[i] = a;
          ans += a;
        }
      } else {
        s[i] = a;
        ans += a;
      }
      count++;
    }
  }
  cout << count << endl;
  cout << ans << endl;
  return 0;
}