import groovy.transform.Memoized

n = 100
m = 100
x1 = 60
y1 = 60

@Memoized
BigInteger solve(int x, int y, int k) {
    if (k == 0) {
        return ((x == x1) && (y == y1)) ? 1g : 0g
    }
    else {
        def up    = (y+1 <  m) ? solve(x, y+1, k-1) : 0g
        def down  = (y-1 >= 0) ? solve(x, y-1, k-1) : 0g
        def right = (x+1 <  n) ? solve(x+1, y, k-1) : 0g
        def left  = (x-1 >= 0) ? solve(x-1, y, k-1) : 0g

        return up + down + left + right
    }
}

println solve(50, 50, 200)