CF271B Prime Matrix

You've got an $ n×m $ matrix. The matrix consists of integers. In one move, you can apply a single transformation to the matrix: choose an arbitrary element of the matrix and increase it by $ 1 $ . Each element can be increased an arbitrary number of times. You are really curious about prime numbers. Let us remind you that a prime number is a positive integer that has exactly two distinct positive integer divisors: itself and number one. For example, numbers 2, 3, 5 are prime and numbers 1, 4, 6 are not. A matrix is prime if at least one of the two following conditions fulfills: - the matrix has a row with prime numbers only; - the matrix has a column with prime numbers only; Your task is to count the minimum number of moves needed to get a prime matrix from the one you've got.

The first line contains two integers $ n,m $ $ (1

Print a single integer — the minimum number of moves needed to get a prime matrix from the one you've got. If you've got a prime matrix, print 0.

In the first sample you need to increase number 1 in cell (1, 1). Thus, the first row will consist of prime numbers: 2, 2, 3. In the second sample you need to increase number 8 in cell (1, 2) three times. Thus, the second column will consist of prime numbers: 11, 2. In the third sample you don't have to do anything as the second column already consists of prime numbers: 3, 2.