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;
char chars[3] = {'A', 'B', 'C'};
int main() {
  int n, k;
  cin >> n >> k;
  string second, s1, s2;
  string ans;
  string tmp;
  cin >> second;
  char prev, prev2;
  int moves = 0, moves2 = 0;
  if (k == 2) {
    for (int i = 0; i < n; i++) {
      if (i == 0)
        prev = second[i];
      else {
        if (second[i] == prev) {
          moves++;
          prev = (second[i] == 'A' ? 'B' : 'A');
        } else
          prev = second[i];
      }
      s1.push_back(prev);
    }
    for (int i = 0; i < n; i++) {
      if (i == 0)
        prev2 = (second[i] == 'A' ? 'B' : 'A'), moves2++;
      else {
        if (second[i] == prev2) {
          prev2 = (second[i] == 'A' ? 'B' : 'A');
          moves2++;
        } else
          prev2 = second[i];
      }
      s2.push_back(prev2);
    }
    if (moves2 < moves) {
      cout << moves2 << endl;
      cout << s2 << endl;
    } else {
      cout << moves << endl;
      cout << s1 << endl;
    }
    return 0;
  } else {
    prev = second[0];
    for (int i = 1; i < n; i++) {
      if (second[i] == second[i - 1]) {
        for (int j = 0; j < 3; j++) {
          if (i + 1 < n) {
            if (chars[j] != second[i - 1] && chars[j] != second[i + 1]) {
              moves++;
              prev = chars[j];
              second[i] = chars[j];
              break;
            }
          } else {
            if (chars[j] != second[i - 1]) {
              moves++;
              prev = chars[j];
              second[i] = chars[j];
              break;
            }
          }
        }
      }
    }
  }
  cout << moves << endl;
  cout << second << endl;
  return 0;
}