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 inf = 0x3fffffff;
char s[500010];
int dp[500010][30];
int len, k;
void change(char &cc, char a, char b) {
  for (int i = 0; i < k; i++)
    if (i + 'A' != a && i + 'A' != b) {
      cc = i + 'A';
      break;
    }
}
int main() {
  while (scanf("%d%d", &len, &k) == 2) {
    scanf("%s", s);
    int t = 0;
    if (k == 2) {
      int t1 = 0, t2 = 0;
      for (int i = 0; i < len; i++)
        if (s[i] != i % 2 + 'A') t1++;
      for (int i = 0; i < len; i++)
        if (s[i] != (i + 1) % 2 + 'A') t2++;
      if (t1 > t2) {
        printf("%d\n", t2);
        for (int i = 0; i < len; i++) putchar((i + 1) % 2 + 'A');
        puts("");
      } else {
        printf("%d\n", t1);
        for (int i = 0; i < len; i++) putchar(i % 2 + 'A');
        puts("");
      }
      continue;
    }
    for (int i = 0; i < len; i++)
      if (i + 1 < len && s[i] == s[i + 1])
        t++, change(s[i + 1], s[i], s[i + 2]);
    printf("%d\n%s\n", t, s);
  }
  return 0;
}