Problem:
Score : 600 points

Problem Statement

Consider the following arithmetic progression with n terms:

x, x + d, x + 2d, \ldots, x + (n-1)d

What is the product of all terms in this sequence?
Compute the answer modulo 1\ 000\ 003.

You are given Q queries of this form.
In the i-th query, compute the answer in case x = x_i, d = d_i, n = n_i.

Constraints

1 \leq Q \leq 10^5

0 \leq x_i, d_i \leq 1\ 000\ 002

1 \leq n_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

Q
x_1 d_1 n_1
:
x_Q d_Q n_Q

Output

Print Q lines.

In the i-th line, print the answer for the i-th query.

Sample Input 1

2
7 2 4
12345 67890 2019

Sample Output 1

9009
916936

For the first query, the answer is 7 \times 9 \times 11 \times 13 = 9009.
Don't forget to compute the answer modulo 1\ 000\ 003.

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

var GET=(function(){function f(s){return new g(s);}function g(s){this._s=s.trim().split("\n");this._y=0;}g.prototype.a=function(f){var s=this._s, y=this._y, r;if(typeof s[y]==="string")s[y]=s[y].split(" ").reverse();r=s[y].pop();if(!s[y].length)this._y++;return f?r:+r;};g.prototype.l=function(f){var s=this._s[this._y++].split(" ");return f?s:s.map(a=>+a);};g.prototype.m=function(n,f){var r=this._s.slice(this._y,this._y+=n).map(a=>a.split(" "));return f?r:r.map(a=>a.map(a=>+a));};g.prototype.r=function(n,f){var r=this._s.slice(this._y,this._y+=n);return f?r:r.map(a=>+a);};return f;})();
var o=GET(require("fs").readFileSync("/dev/stdin","utf8"));
function xArray(v){var a=arguments,l=a.length,r="Array(a["+--l+"]).fill(0).map(x=>{return "+v+";})";while(--l)r="Array(a["+l+"]).fill(0).map(x=>"+r+")";return eval(r);}
var mod = 1000003;
function abmod(){for(var a=arguments,r=a[0],i=1;i<a.length;)r=((r>>16)*a[i]%mod*65536+(r&65535)*a[i++])%mod;return r;}
var fac=[1,1];
function fSet(n){for(var i=2;i<=n;)fac[i]=abmod(fac[i-1],i++);}
function modinv(a){for(var b=mod,u=1,v=0,t;b;v=t)t=a/b|0,a-=t*b,u-=t*v,t=a,a=b,b=t,t=u,u=v;u%=mod;return u<0?u+mod:u;}
function nPrmod(n,r){return abmod(fac[n],modinv(fac[(n-r+mod)%mod]));}
function powmod(a,n){for(var r=1;n;a=abmod(a,a),n>>=1)if(n&1)r=abmod(a,r);return r;}

console.log(main());
function main(){
  var q = o.a();
  var ans = Array(q).fill(0);
  fSet(mod);
  for(var i = 0; i < q; i++){
    var t = o.l(), x = t[0], d = t[1], n = t[2];
    if(x === 0)continue;
    if(d === 0){
      ans[i] = powmod(x,n);
    }else{
      if(n >= mod)continue;
      var u = (mod-x)/d;
      var g = exgcd(mod,d);
      var u = ((mod-x)*g[1]%mod+mod)%mod;
      if(u < n)continue;
      var a = ((mod-abmod(x,modinv(d)))%mod+mod)%mod;
      var p = nPrmod(a,n);
      var m = powmod(mod-d,n);
      ans[i] = abmod(p,m);
    }
  }
  return ans.join("\n");
}

function exgcd(x,y){
  var r0 = x, r1 = y, a0 = 1, a1 = 0, b0 = 0, b1 = 1;
  while(r1){
    var q1 = r0 / r1 | 0;
    var r2 = r0 % r1;
    var a2 = a0 - q1*a1;
    var b2 = b0 - q1*b1
    r0 = r1, r1 = r2;
    a0 = a1, a1 = a2;
    b0 = b1, b1 = b2;
  }
  return [a0,b0,r0];
}