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;
void read_file(bool outToFile = true) {}
int n, K;
string s;
string anss;
int ansn;
char next(char x, char y) {
  for (int i = 0; i < 3; i++)
    if (i + 'A' != x && i + 'A' != y) return i + 'A';
}
int main() {
  read_file();
  while (cin >> n >> K) {
    cin >> s;
    if (K == 2) {
      ansn = n + 1;
      string nws(n, ' ');
      int nwn = 0;
      for (int i = 0; i < n; i++) {
        nws[i] = i % 2 == 0 ? 'A' : 'B';
        nwn += nws[i] != s[i];
      }
      if (nwn < ansn) ansn = nwn, anss = nws;
      nwn = 0;
      for (int i = 0; i < n; i++) {
        nws[i] = i % 2 == 0 ? 'B' : 'A';
        nwn += nws[i] != s[i];
      }
      if (nwn < ansn) ansn = nwn, anss = nws;
    } else {
      ansn = 0;
      for (int i = 1; i < n; i++) {
        if (s[i] == s[i - 1])
          s[i] = next(s[i - 1], (i + 1 < n ? s[i + 1] : ' ')), ansn++;
      }
      anss = s;
    }
    cout << ansn << '\n';
    cout << anss << '\n';
  }
}