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;
template <class T>
typename T::value_type arr_sum(const T& v, int n) {
  typename T::value_type sum = 0;
  for (int i = (0); i < (n); ++i) sum += v[i];
  return sum;
}
struct Sync_stdio {
  Sync_stdio() {
    cin.tie(NULL);
    ios_base::sync_with_stdio(false);
  }
} _sync_stdio;
char f(char a, char b) {
  for (int i = ('A'); i < ('D'); ++i) {
    if (a != i && b != i) {
      return i;
    }
  }
  return 42;
}
int main() {
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;
  if (k == 2) {
    string s1, s2;
    for (int i = (0); i < (n); ++i) {
      s1 += ('A' + i % 2);
      s2 += ('A' + (i + 1) % 2);
    }
    int a1 = 0, a2 = 0;
    for (int i = (0); i < (n); ++i) {
      if (s[i] == s1[i]) {
        ++a1;
      } else {
        ++a2;
      }
    }
    if (a1 > a2) {
      cout << a2 << "\n";
      cout << s1;
    } else {
      cout << a1 << "\n";
      cout << s2;
    }
    return 0;
  }
  int res = 0;
  s += '.';
  for (int i = (1); i < (n); ++i) {
    if (s[i] == s[i - 1]) {
      s[i] = f(s[i - 1], s[i + 1]);
      ++res;
    }
  }
  s.pop_back();
  cout << res << "\n";
  cout << s;
}