Given a number line from 0 to n and a string denoting a sequence of moves, determine the number of subsequences of those moves that lead from a given point x to end at another point y. Moves will be given as a sequence of l and r instructions. An instruction l = left movement, so from position j the new position is j - 1, an instruction r = right movement, so from position j the new position would be j + 1.

For example, given a number line from 0 to 6, and a sequence of moves rrlrr, the number of subsequences that lead from 1 to 4 on the number line is 3.

Function Description

Complete the function distinctMoves in the editor.

distinctMoves has the following parameter(s):

1. s: a string that represents a sequence of moves
2. n: an integer that represents the upper bound of the number line
3. x: an integer that represents the starting point
4. y: an integer that represents the ending point

Returns

int: the number of distinct subsequences modulo 10^9 + 7