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() {
  ios_base::sync_with_stdio;
  cin.tie(0);
  cout.tie(0);
  int ans = 0;
  string cad;
  string copyA;
  string copyB;
  int colors;
  int tam;
  int min = 0;
  int aux = 0;
  cin >> tam >> colors >> cad;
  if (colors == 2) {
    copyA = cad;
    copyB = cad;
    for (int i = 0; i < tam; ++i) {
      if (i % 2 == 0) {
        if (cad[i] != 'A') {
          aux++;
          copyA[i] = 'A';
        }
      }
      if (i % 2 == 1) {
        if (cad[i] != 'B') {
          aux++;
          copyA[i] = 'B';
        }
      }
    }
    for (int i = 0; i < tam; ++i) {
      if (i % 2 == 0) {
        if (cad[i] != 'B') {
          min++;
          copyB[i] = 'B';
        }
      }
      if (i % 2 == 1) {
        if (cad[i] != 'A') {
          min++;
          copyB[i] = 'A';
        }
      }
    }
    if (min < aux) {
      cout << min << '\n';
      cout << copyB;
    } else {
      cout << aux << '\n';
      cout << copyA;
    }
  } else {
    for (int i = 1; i < tam; ++i) {
      if (cad[i] == cad[i - 1]) {
        if (i + 1 < tam) {
          if ('A' != cad[i - 1] and 'A' != cad[i + 1]) {
            cad[i] = 'A';
            ans++;
          } else if ('B' != cad[i - 1] and 'B' != cad[i + 1]) {
            cad[i] = 'B';
            ans++;
          } else if ('C' != cad[i - 1] and 'C' != cad[i + 1]) {
            cad[i] = 'C';
            ans++;
          }
        } else {
          if ('A' != cad[i - 1]) {
            cad[i] = 'A';
            ans++;
          } else if ('B' != cad[i - 1]) {
            cad[i] = 'B';
            ans++;
          } else if ('C' != cad[i - 1]) {
            cad[i] = 'C';
            ans++;
          }
        }
      }
    }
    cout << ans << '\n';
    cout << cad;
  }
  return 0;
}