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 = 500000 + 5;
int dp[maxn][26], pre[maxn][26];
char s[maxn];
void print(int i, int j) {
  if (i == -1) {
    return;
  }
  print(i - 1, pre[i][j]);
  printf("%c", j + 'A');
}
int main(void) {
  int n, k;
  scanf("%d%d", &n, &k);
  scanf("%s", s);
  for (int j = 0; j < k; j++) {
    dp[0][j]++;
  }
  dp[0][s[0] - 'A']--;
  memset(pre, -1, sizeof(pre));
  for (int i = 1; i < n; i++) {
    for (int j = 0; j < k; j++) {
      int mi = maxn, who = -1;
      for (int p = 0; p < k; p++) {
        if (p != j) {
          int tmp = dp[i - 1][p] + (s[i] - 'A' == j ? 0 : 1);
          if (tmp < mi) {
            mi = tmp;
            who = p;
          }
        }
      }
      dp[i][j] = mi;
      pre[i][j] = who;
    }
  }
  int pos = min_element(dp[n - 1], dp[n - 1] + k) - dp[n - 1];
  printf("%d\n", dp[n - 1][pos]);
  print(n - 1, pos);
  return 0;
}