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 INF = 0x3f3f3f3f;
const int maxn = 5e5 + 10;
const int maxk = 30;
int n, k;
char in[maxn], out[maxn];
int dp[maxn][maxk];
int pre[maxn][maxk];
int main() {
  cin >> n >> k;
  scanf("%s", in + 1);
  for (int i = 1; i <= n; i++) {
    for (int v = 1; v <= k; v++) {
      dp[i][v] = INF;
      int flag = (in[i] - 'A' + 1 != v);
      for (int u = 1; u <= k; u++) {
        if (u == v) continue;
        if (dp[i][v] > dp[i - 1][u] + flag) {
          dp[i][v] = dp[i - 1][u] + flag;
          pre[i][v] = u;
        }
      }
    }
  }
  int ans = INF, clr;
  for (int i = 1; i <= k; i++)
    if (ans > dp[n][i]) ans = dp[n][i], clr = i;
  printf("%d\n", ans);
  for (int i = n; i >= 1; i--) out[i] = 'A' + clr - 1, clr = pre[i][clr];
  printf("%s\n", out + 1);
}