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;
int dp[maxN + 1][26];
short parent[maxN + 1][26];
int main() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  s = '$' + s;
  s += '$';
  for (int j = 'A'; j <= 'A' + k - 1; j++) {
    if (j == s[0]) {
      continue;
    }
    dp[1][j - 'A'] = 1;
  }
  dp[1][s[1] - 'A'] = 0;
  for (int i = 2; i <= n; i++) {
    for (int j = 'A'; j <= 'A' + k - 1; j++) {
      dp[i][j - 'A'] = 1e9;
      for (int j2 = 'A'; j2 <= 'A' + k - 1; j2++) {
        if (j != j2) {
          if (j == s[i]) {
            if (dp[i][j - 'A'] > dp[i - 1][j2 - 'A']) {
              dp[i][j - 'A'] = dp[i - 1][j2 - 'A'];
              parent[i][j - 'A'] = j2 - 'A';
            }
          } else {
            if (dp[i][j - 'A'] > dp[i - 1][j2 - 'A'] + 1) {
              dp[i][j - 'A'] = dp[i - 1][j2 - 'A'] + 1;
              parent[i][j - 'A'] = j2 - 'A';
            }
          }
        }
      }
    }
  }
  int minval = 1e9, id = -1;
  for (int i = 'A'; i <= 'A' + k - 1; i++) {
    if (minval > dp[n][i - 'A']) {
      minval = dp[n][i - 'A'];
      id = i - 'A';
    }
  }
  cout << minval << endl;
  string t = "";
  for (int i = n; i >= 1; i--) {
    t += (char)(id + 'A');
    id = parent[i][id];
  }
  reverse(t.begin(), t.end());
  cout << t;
}