B"There are n boxes placed in a line. The boxes are numbered from 1 to n . Some boxes contain one ball inside of them, the rest are empty. At least one box contains a ball and at least one box is empty. In one move, you have to choose a box with a ball inside and an adjacent empty box and move the ball from one box into another. Boxes i and i+1 for all i from 1 to n-1 are considered adjacent to each other. Boxes 1 and n are not adjacent. How many different arrangements of balls exist after exactly k moves are performed? Two arrangements are considered different if there is at least one such box that it contains a ball in one of them and doesn't contain a ball in the other one. Since the answer might be pretty large, print its remainder modulo 10^9+7 . The first line contains two integers n and k ( 2 <= n <= 1500 ; 1 <= k <= 1500 ) -- the number of boxes and the number of moves. The second line contains n integers a_1, a_2, ... , a_n ( a_i in {0, 1 } ) -- 0 denotes an empty box and 1 denotes a box with a ball inside. There is at least one 0 and at least one 1 . Print a single integer -- the number of different arrangements of balls that can exist after exactly k moves are performed, modulo 10^9+7 . In the first example, there are the following possible arrangements: In the second example, there are the following possible arrangements: "...