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[5 * 100000 + 1][26];
char previous[5 * 100000 + 1][26];
int main() {
  int n, a;
  string s;
  cin >> n >> a >> s;
  for (int c = 0; c < a; ++c) dp[0][c] = 0;
  for (int i = 0; i < n; ++i) {
    const int c = s[i] - 'A';
    for (int j = 0; j < a; ++j) {
      int res = 100000000;
      for (int k = 0; k < a; ++k) {
        if (j == k) continue;
        if (dp[i][k] < res) {
          res = dp[i][k];
          previous[i + 1][j] = k;
        }
      }
      dp[i + 1][j] = res + (c != j);
    }
  }
  int pos = min_element(dp[n] + 0, dp[n] + a) - (dp[n] + 0);
  cout << dp[n][pos] << endl;
  for (int i = n - 1; i >= 0; --i) {
    s[i] = pos + 'A';
    pos = previous[i + 1][pos];
  }
  cout << s << endl;
}