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 long long INF = 1e9;
const long long N = 5e5 + 1;
const long long mod = 1e9 + 7;
const long double eps = 1E-7;
char a[N];
int n, m, f;
int d[N][26];
int p[N][26];
void rec(int i, int k) {
  if (i == 0) return;
  rec(i - 1, p[i][k]);
  cout << char(k + 'A');
}
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> m;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    a[i] -= 'A';
    if (i == 1) {
      for (int j = 0; j < m; j++) d[1][j] = j != a[i];
      continue;
    }
    for (int j = 0; j < m; j++) {
      d[i][j] = INF;
      f = (j != a[i]);
      for (int h = 0; h < m; h++) {
        if (j == h) continue;
        if (d[i - 1][h] + f < d[i][j]) {
          p[i][j] = h;
          d[i][j] = d[i - 1][h] + f;
        }
      }
    }
  }
  f = 0;
  for (int i = 0; i < m; i++)
    if (d[n][f] > d[n][i]) f = i;
  cout << d[n][f] << endl;
  rec(n, f);
}