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 dp[2][26];
char pt[500001][26], s[500001];
int main() {
  int n, K, id;
  scanf("%d %d %s", &n, &K, s);
  int p = 0;
  for (int i = 0; i < K; ++i) {
    if (s[0] - 'A' == i)
      dp[p][i] = 0;
    else
      dp[p][i] = 1;
    pt[1][i] = -1;
  }
  for (int i = 2; i <= n; ++i) {
    p = p ^ 1;
    for (int j = 0; j < K; ++j) {
      dp[p][j] = INT_MAX;
      for (int k = 0; k < K; ++k) {
        if (j != k) {
          if (s[i - 1] - 'A' == j) {
            if (dp[p][j] > dp[p ^ 1][k]) {
              dp[p][j] = dp[p ^ 1][k];
              id = k;
            }
          } else {
            if (dp[p][j] > dp[p ^ 1][k] + 1) {
              dp[p][j] = dp[p ^ 1][k] + 1;
              id = k;
            }
          }
        }
      }
      pt[i][j] = id;
    }
  }
  int ans = INT_MAX;
  for (int i = 0; i < K; ++i) {
    if (ans > dp[p][i]) {
      ans = dp[p][i];
      id = i;
    }
  }
  printf("%d\n", ans);
  string res = "";
  int l = n;
  while (id != -1) {
    res += char(id + 'A');
    id = pt[l][id];
    l--;
  }
  for (int i = n - 1; i >= 0; --i) {
    putchar(res[i]);
  }
  return 0;
}