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;
const int maxn = 5e5 + 10;
int n, m;
char a[maxn];
int main() {
  while (~scanf("%d%d", &n, &m)) {
    scanf("%s", a);
    if (m != 2) {
      int cnt = 0;
      for (int i = 1; i < n; i++) {
        if (a[i - 1] == a[i]) {
          a[i] = 'A';
          while (1) {
            if (a[i - 1] != a[i] && a[i] != a[i + 1]) break;
            a[i]++;
          }
          cnt++;
        }
      }
      printf("%d\n", cnt);
      printf("%s\n", a);
    } else {
      int cntA = 0, cntB = 0;
      for (int i = 0; i < n; i++) {
        if (i % 2 == 0) {
          if (a[i] == 'A')
            cntB++;
          else
            cntA++;
        } else {
          if (a[i] == 'B')
            cntB++;
          else
            cntA++;
        }
      }
      if (cntA < cntB) {
        printf("%d\n", cntA);
        for (int i = 0; i < n; i++) {
          if (i % 2 == 0)
            printf("A");
          else
            printf("B");
        }
        printf("\n");
      } else {
        printf("%d\n", cntB);
        for (int i = 0; i < n; i++) {
          if (i % 2 == 1)
            printf("A");
          else
            printf("B");
        }
        printf("\n");
      }
    }
  }
  return 0;
}