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 JAVA):

Solution:
print(function(n, k) {
	var s = readline().split('');
	if (k == 2) {
		var a1 = [];
		var a2 = [];
		var c1 = 0;
		var c2 = 0;
		for (var i = 0; i < n; i++) {
			var x1 = i % 2 ? 'A' : 'B';
			var x2 = i % 2 ? 'B' : 'A';
			a1.push(x1);
			a2.push(x2);
			if (s[i] !== x1) c1++;
			if (s[i] !== x2) c2++;
		}
		if (c1 > c2)
			return c2 + '\n' + a2.join('');
		return c1 + '\n' + a1.join('');
	}

	var ans = 0;
	for (var i = 1; i < n; i++)
		if (s[i] === s[i - 1]) {
			ans++;
			if (s[i - 1] === 'A' || s[i + 1] === 'A')
				if (s[i - 1] === 'B' || s[i + 1] === 'B')
					s[i] = 'C';
				else
					s[i] = 'B';
			else
				s[i] = 'A';
		}

	return ans + '\n' + s.join('')

}.apply(0, readline().split(' ').map(Number)));