java - calculate the modulus of a fraction with big numbers -

i have 2 big numbers (<10^9) n , m. have calculate [(n-1+m)!]/[(n-1)!*m!] if answer big have modulus (10^9+7). (ex : n%mod if n large mod).

 int mod = 1000000000+7; 

i calculated below. (i calculated upper half , bottom half separately)

    long up=1;     (long = a+b-1; i>=math.max(a, b); i--) {         up*=i%mod;                 }     up=up%mod;     long down=1;     (long = math.min(a, b); i>0; i--) {         down*=i%mod;                 } 

then print answer

system.out.println((up%mod/down%mod)%mod); 

is approach correct. gives correct out put.

i know (a*b*c)%d == [(a%d)*(b%d)*(c%d)]%d (correct me if i'm wrong)

so there way calculate [a/b]%d ?

(a/b) % c != ((a%c) / (b%c) % c) 

instead use recursive formula of binomial coefficient calculate modulus

(n, k) = (n - 1, k - 1) + (n - 1, k) 

in case be

(n - 1 + m, m) % mod = ((n - 2 + m, m - 1) % mod + (n - 2 + m, m) % mod) % mod 

use above recursion result.