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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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