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 MAXL = 500001, inf = 1000000;
char str[MAXL], ansset[MAXL];
int f[MAXL][26], inverse[MAXL][26], g[MAXL][26];
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  scanf("%s", str);
  for (int i = 0; i < n; ++i)
    for (int j = 0; j < 26; ++j) f[i][j] = inf;
  for (int j = 0; j < 26; ++j) f[0][j] = 1;
  f[0][str[0] - 'A'] = 0;
  for (int i = 1; i < n; ++i) {
    for (int j = 0; j < k; ++j) {
      int cost = ((str[i] - 'A') != j);
      for (int l = 0; l < k; ++l)
        if (l != j) {
          if (f[i][j] > f[i - 1][l] + cost) {
            f[i][j] = min(f[i][j], f[i - 1][l] + cost);
            g[i][j] = l;
          }
        }
    }
  }
  int ans = inf, tmp;
  for (int j = 0; j < k; ++j)
    if (f[n - 1][j] < ans) ans = f[n - 1][j], tmp = j;
  printf("%d\n", ans);
  int top = 0;
  for (int i = n - 1; i >= 0; --i) {
    ansset[top++] = tmp + 'A';
    tmp = g[i][tmp];
  }
  while (top) {
    --top;
    printf("%c", ansset[top]);
  }
  printf("\n");
  return 0;
}