hdu 2576 Another Sum Problem 水題

/*
hdu 2576 Another Sum Problem
1^2+2^2+3^2...   n(n+1)(2n+1)/6
公式很好推
n(n+1)(n+2)/6
但是爲什麼需要先/2然後再/3呢？求解答
*/
#include<stdio.h>
#define N 20090524
int main()
{
	__int64 t,a,ret;
	scanf("%I64d",&t);
	while(t--)
	{
		scanf("%I64d",&a);
		a=a%N;
		ret=(a*(a+1))/2%(N*3);
		ret=(ret*(a+2))/3%N;
		printf("%I64d\n",ret);
	}
	return 0;
}