Array Initialization

Many programming languages have functions that fill an entire array, or part of it, with a given value. In Pascal this is fillchar(), in Java it is Arrays.fill(), and in C++ it is memset(). The new programming language J# has a function mark() that works only with boolean arrays.

Called with two parameters $a$ and $b$, mark assigns true to every element of the array with index from $a$ to $b$ inclusive. For example, take an array of length 4 whose elements are numbered from one and whose values are all initially false. Running mark(1, 3) and then mark(2, 4) on it fills the whole array with true.

One of the first assignments for people starting to learn J# is to write a program that contains exactly $M$ mark operations and completely fills an array of length $N$, initially filled with false, with true.

You solved this assignment quickly, and now you wonder: in how many different ways can this be done? Two programs are considered different if the $i$-th mark operation is run with different parameters in them for at least one $i$ from 1 to $M$. This number can be large, so you need to compute it modulo $10^9+7$.

The first line of the input file contains two positive integers $N$ and $M$: the length of the array and the number of mark operations the program must contain. ($1 \le N, M \le 70$)

In a single line of the output file, print the remainder modulo $10^9+7$ of the number of ways to fill an array of $N$ elements with true using $M$ calls of the mark operation.

The required variants:

• mark(1, 1); mark(1, 2)
• mark(1, 1); mark(2, 2)
• mark(1, 2); mark(1, 1)
• mark(1, 2); mark(1, 2)
• mark(1, 2); mark(2, 2)
• mark(2, 2); mark(1, 1)
• mark(2, 2); mark(1, 2)