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 MAX = 2e5 + 7;
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  string str;
  cin >> n >> k;
  cin >> str;
  vector<vector<int> > dp(n + 1, vector<int>(26, INT_MAX));
  vector<vector<int> > dp2(n + 1, vector<int>(26, -1));
  for (int i = 0; i < k; i++) {
    dp[0][i] = str[0] - 'A' == i ? 0 : 1;
  }
  for (int curPos = 1; curPos < n; curPos++) {
    for (int prevCol = 0; prevCol < k; prevCol++) {
      dp[curPos][prevCol] = INT_MAX;
      for (int i = 0; i < k; i++) {
        if (i != prevCol) {
          int temp = str[curPos] - 'A' == prevCol ? 0 : 1;
          int curAns = dp[curPos - 1][i] + temp;
          if (dp[curPos][prevCol] > curAns) {
            dp2[curPos][prevCol] = i;
            dp[curPos][prevCol] = curAns;
          }
        }
      }
    }
  }
  int ans = INT_MAX, start;
  for (int i = k - 1; i >= 0; i--) {
    if (ans > dp[n - 1][i]) {
      ans = dp[n - 1][i];
      start = i;
    }
  }
  cout << ans << endl;
  string s = "";
  int i = n - 1;
  while (i >= 0) {
    s += start + 'A';
    start = dp2[i--][start];
  }
  reverse(s.begin(), s.end());
  cout << s;
}