Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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C. Color Stripe

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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* ≤ 5·10^{5}; 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

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