2017/finals/patrols.cpp

// Hacker Cup 2017
// Final Round
// Fox Patrols
// Jacob Plachta

#include <algorithm>
#include <functional>
#include <numeric>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <complex>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <cassert>
#include <string>
#include <vector>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <stack>
#include <bitset>
#include <sstream>
using namespace std;

#define LL long long
#define LD long double
#define PR pair<int,int>

#define Fox(i,n) for (i=0; i<n; i++)
#define Fox1(i,n) for (i=1; i<=n; i++)
#define FoxI(i,a,b) for (i=a; i<=b; i++)
#define FoxR(i,n) for (i=(n)-1; i>=0; i--)
#define FoxR1(i,n) for (i=n; i>0; i--)
#define FoxRI(i,a,b) for (i=b; i>=a; i--)
#define Foxen(i,s) for (i=s.begin(); i!=s.end(); i++)
#define Min(a,b) a=min(a,b)
#define Max(a,b) a=max(a,b)
#define Sz(s) int((s).size())
#define All(s) (s).begin(),(s).end()
#define Fill(s,v) memset(s,v,sizeof(s))
#define pb push_back
#define mp make_pair
#define x first
#define y second

template<typename T> T Abs(T x) { return(x<0 ? -x : x); }
template<typename T> T Sqr(T x) { return(x*x); }

const int INF = (int)1e9;
const LD EPS = 1e-12;
const LD PI = acos(-1.0);

bool Read(int &x)
{
	char c,r=0,n=0;
	x=0;
		for(;;)
		{
			c=getchar();
				if ((c<0) && (!r))
					return(0);
				if ((c=='-') && (!r))
					n=1;
				else
				if ((c>='0') && (c<='9'))
					x=x*10+c-'0',r=1;
				else
				if (r)
					break;
		}
		if (n)
			x=-x;
	return(1);
}

#define MOD 1000000007

// a^b
int pw(LL a,int b)
{
	int v=1;
		while (b)
		{
				if (b&1)
					v=v*a%MOD;
			a=a*a%MOD;
			b>>=1;
		}
	return(v);
}

// number of skylines of length n with max height h
LL cnt(int n,int h)
{
	return((pw(h,n)-pw(h-1,n)+MOD)%MOD);
}

int main()
{
	// vars
	int T,t;
	int N,M,H;
	int h,ans;
	// testcase loop
	Read(T);
		Fox1(t,T)
		{
			// input
			Read(N),Read(M),Read(H);
			// consider all possible max tree heights
			ans=0;
				Fox1(h,H)
					ans=(ans+cnt(N,h)*cnt(M,h))%MOD;
			// output
			printf("Case #%d: %d\n",t,ans);
		}
	return(0);
}