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;
#pragma comment(linker, "/STACK:400000000")
int n, k, dp[500010][28], best[500010][28];
string s;
int f(int cur, int pre) {
  int& res = dp[cur][pre];
  if (res > -1) return res;
  if (cur == n) return res = 0;
  res = 1000000007LL;
  if (pre != s[cur] - 'A') {
    res = f(cur + 1, s[cur] - 'A');
    best[cur][pre] = s[cur];
  }
  vector<int> next;
  int newC = 0;
  while ((newC == pre || newC == s[cur + 1] - 'A') && newC < k) newC++;
  if (newC < k) next.push_back(newC);
  if (pre != s[cur + 1] - 'A') next.push_back(s[cur + 1] - 'A');
  for (int i = 0; i < next.size(); i++) {
    int res2 = f(cur + 1, next[i]) + 1;
    if (res2 < res) {
      res = res2;
      best[cur][pre] = next[i] + 'A';
    }
  }
  return res;
}
void g(int cur, int pre) {
  if (cur == n) return;
  cout << (char)best[cur][pre];
  g(cur + 1, best[cur][pre] - 'A');
}
int main() {
  cin >> n >> k >> s;
  s += (char)('Z' + 1);
  memset(dp, -1, sizeof(dp));
  cout << f(0, 26) << endl;
  g(0, 26);
}