Actually the answer is

(m+n-1)C(n)=(m+n-1)!/ ((m-1)!)*n!)

and the forumula

Ncr=(n-1)c(r-1)+ (n-1)c(r)

now you can apply dp you may take help of this function as it is little bit tuff for me to understand c# that's why iam writing this function

`cpp

for (i = 0; i <= n; i++) { for (j = 0; j <= k; j++) {

        if (j == 0 || j == i)//as nc0=ncn=1;
            C[i][j] = 1;


     else
       C[i][j] = ((C[i-1][j-1])%mod +( C[i-1][j])%mod)%mod;
    }
}

`

now you can return the desired answer .

Now in your code this line

result = (topfact / (belowfact1 * belowfact2))%1000000007; will get run-time error or tle as your modulus approach formula is not correct as

(a * b) % mod = ((a % mod) * (b % mod)) % mod, (a / b ) % mod = ((a % mod) * (b^-1 % mod)) % mod,

and one more reason is that the

(topfact / (belowfact1*belowfact2))

will not work properly .

if problem persist then feel free to contact for further

clarification or you may take help of my c code

http://ideone.com/knhd1k

....

Hey take a look at this if it helps

from math import factorial

n=int(raw_input())
for i in range(n):
    a,b=map(int,raw_input().split())
    print (factorial(a+b-1)/(factorial(a)*factorial(b-1)))%1000000007

I believe if you try with N=1000 and M=1000, you will get the run time error. Basically, 1000!*999>ulong.MAX, in other words, it should give you kind of overflow.

logic is simple there are total m 1's and n 0's now you fix one 1 at starting of the string so you have m-1 1's now we have arrange them m+n-1!/(m-1!)(n!)