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 n, k, pre[500010][26];
int first[500010][26];
char second[500010];
int main() {
  scanf("%d%d%s", &n, &k, second);
  memset(first, 0x3f, sizeof(first));
  for (int i = 0; i < k; i++) {
    if (i != second[0] - 'A')
      first[0][i] = 1;
    else
      first[0][i] = 0;
  }
  for (int i = 0; i < n - 1; i++) {
    for (int j = 0; j < k; j++)
      if (first[i][j] < 0x3f3f3f3f) {
        for (int x = 0; x < k; x++)
          if (x != j) {
            if (x == second[i + 1] - 'A') {
              if (first[i][j] < first[i + 1][x]) {
                first[i + 1][x] = first[i][j];
                pre[i + 1][x] = j;
              }
            } else {
              if (first[i][j] + 1 < first[i + 1][x]) {
                first[i + 1][x] = first[i][j] + 1;
                pre[i + 1][x] = j;
              }
            }
          }
      }
  }
  int c, ans = 0x3f3f3f3f;
  for (int i = 0; i < k; i++)
    if (first[n - 1][i] < ans) {
      ans = first[n - 1][i];
      c = i;
    }
  second[n - 1] = c + 'A';
  for (int i = n - 1; i > 0; i--) {
    second[i - 1] = pre[i][c] + 'A';
    c = pre[i][c];
  }
  cout << ans << endl;
  cout << second << endl;
  return 0;
}