fbe763b30e 2016-05-26        kinaba: #include <iostream>
fbe763b30e 2016-05-26        kinaba: #include <sstream>
fbe763b30e 2016-05-26        kinaba: #include <iomanip>
fbe763b30e 2016-05-26        kinaba: #include <vector>
fbe763b30e 2016-05-26        kinaba: #include <string>
fbe763b30e 2016-05-26        kinaba: #include <map>
fbe763b30e 2016-05-26        kinaba: #include <set>
fbe763b30e 2016-05-26        kinaba: #include <algorithm>
fbe763b30e 2016-05-26        kinaba: #include <numeric>
fbe763b30e 2016-05-26        kinaba: #include <iterator>
fbe763b30e 2016-05-26        kinaba: #include <functional>
fbe763b30e 2016-05-26        kinaba: #include <complex>
fbe763b30e 2016-05-26        kinaba: #include <queue>
fbe763b30e 2016-05-26        kinaba: #include <stack>
fbe763b30e 2016-05-26        kinaba: #include <cmath>
fbe763b30e 2016-05-26        kinaba: #include <cassert>
fbe763b30e 2016-05-26        kinaba: #include <tuple>
fbe763b30e 2016-05-26        kinaba: using namespace std;
fbe763b30e 2016-05-26        kinaba: typedef long long LL;
fbe763b30e 2016-05-26        kinaba: typedef complex<double> CMP;
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: static const unsigned MODVAL = 1000000007;
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: struct mint
fbe763b30e 2016-05-26        kinaba: {
fbe763b30e 2016-05-26        kinaba: 	unsigned val;
fbe763b30e 2016-05-26        kinaba: 	mint():val(0){}
fbe763b30e 2016-05-26        kinaba: 	mint(int      x):val(x%MODVAL) {}
fbe763b30e 2016-05-26        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
fbe763b30e 2016-05-26        kinaba: 	mint(LL       x):val(x%MODVAL) {}
fbe763b30e 2016-05-26        kinaba: };
fbe763b30e 2016-05-26        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
fbe763b30e 2016-05-26        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
fbe763b30e 2016-05-26        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
fbe763b30e 2016-05-26        kinaba: mint operator+(mint x, mint y) { return x+=y; }
fbe763b30e 2016-05-26        kinaba: mint operator-(mint x, mint y) { return x-=y; }
fbe763b30e 2016-05-26        kinaba: mint operator*(mint x, mint y) { return x*=y; }
fbe763b30e 2016-05-26        kinaba: mint POW(mint x, LL e) { mint v=1; for(;e;x*=x,e>>=1) if(e&1) v*=x; return v; }
fbe763b30e 2016-05-26        kinaba: mint& operator/=(mint& x, mint y) { return x *= POW(y, MODVAL-2); }
fbe763b30e 2016-05-26        kinaba: mint operator/(mint x, mint y) { return x/=y; }
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: class TriangleTriples { public:
fbe763b30e 2016-05-26        kinaba: 	int count(int A, int B, int C)
fbe763b30e 2016-05-26        kinaba: 	{
fbe763b30e 2016-05-26        kinaba: 		return (mint(A)*B*C - cut(A,B,C) - cut(B,C,A) - cut(C,A,B)).val;
fbe763b30e 2016-05-26        kinaba: 	}
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: 	// #{(a,b,c)<=(A,B,C) | a+b<=c}
fbe763b30e 2016-05-26        kinaba: 	mint cut(LL A, LL B, LL C)
fbe763b30e 2016-05-26        kinaba: 	{
fbe763b30e 2016-05-26        kinaba: 		if(A>B) swap(A,B);
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: 		//----------------------------
fbe763b30e 2016-05-26        kinaba: 		// Sigma
fbe763b30e 2016-05-26        kinaba: 		// #{a+b <= 1}
fbe763b30e 2016-05-26        kinaba: 		// #{a+b <= 2}
fbe763b30e 2016-05-26        kinaba: 		// ...
fbe763b30e 2016-05-26        kinaba: 		// #{a+b <= C}
fbe763b30e 2016-05-26        kinaba: 		//----------------------------
fbe763b30e 2016-05-26        kinaba: 		// Sigma
fbe763b30e 2016-05-26        kinaba: 		// #{a+b == 1} * C
fbe763b30e 2016-05-26        kinaba: 		// #{a+b == 2} * C-1
fbe763b30e 2016-05-26        kinaba: 		// ...
fbe763b30e 2016-05-26        kinaba: 		// #{a+b == C} * 1
fbe763b30e 2016-05-26        kinaba: 		//----------------------------
fbe763b30e 2016-05-26        kinaba: 		// where
fbe763b30e 2016-05-26        kinaba: 		//
fbe763b30e 2016-05-26        kinaba: 		//  #{a+b == k}
fbe763b30e 2016-05-26        kinaba: 		//=
fbe763b30e 2016-05-26        kinaba: 		//   k-1       for        k <= A
fbe763b30e 2016-05-26        kinaba: 		//   A         for  A+1<= k <= B
fbe763b30e 2016-05-26        kinaba: 		//   A-(k-B)+1 for  B+1<= k <= A+B
fbe763b30e 2016-05-26        kinaba: 		//   0         for  A+B<  k
fbe763b30e 2016-05-26        kinaba: 		//----------------------------
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: 		mint total = 0;
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: 		//for(int k=1; k<=min(C,A); ++k)
fbe763b30e 2016-05-26        kinaba: 		//	total += mint(k-1) * (C-k+1);
fbe763b30e 2016-05-26        kinaba: 		{
fbe763b30e 2016-05-26        kinaba: 			LL x = min(C,A);
fbe763b30e 2016-05-26        kinaba: 			total += mint(0+x-1)*x/2 * C - mint(x-1)*x*(2*x-1)/6;
fbe763b30e 2016-05-26        kinaba: 		}
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: 		// for(int k=A+1; k<=min(C,B); ++k)
fbe763b30e 2016-05-26        kinaba: 		// 	total += mint(A) * (C-k+1);
fbe763b30e 2016-05-26        kinaba: 		if(A+1 <= min(C,B)) {
fbe763b30e 2016-05-26        kinaba: 			LL x = A+1, y = min(C,B);
fbe763b30e 2016-05-26        kinaba: 			total += mint(A) * (C-x+1+C-y+1) * (y-x+1) / 2;
fbe763b30e 2016-05-26        kinaba: 		}
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: 		//for(int k=B+1; k<=min(C,A+B); ++k)
fbe763b30e 2016-05-26        kinaba: 		//	total += mint(A-(k-B)+1) * (C-k+1);
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: 		if(B+1 <= min(C,A+B)) {
fbe763b30e 2016-05-26        kinaba: 			LL X = min(C,A+B)-B, D = C-B;
fbe763b30e 2016-05-26        kinaba: 			//for(LL k=0; k<=X; ++k)
fbe763b30e 2016-05-26        kinaba: 			//	total += mint(A-k)*(D-k);
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: 			LL E = abs(D-A);
fbe763b30e 2016-05-26        kinaba: 			//for(LL k=0; k<=X; ++k)
fbe763b30e 2016-05-26        kinaba: 			//	total += mint(k)*(k+E);
fbe763b30e 2016-05-26        kinaba: 			total += mint(X)*(X+1)/2*E + mint(X)*(X+1)*(2*X+1)/6;
fbe763b30e 2016-05-26        kinaba: 		}
fbe763b30e 2016-05-26        kinaba: 		return total;
fbe763b30e 2016-05-26        kinaba: 	}
fbe763b30e 2016-05-26        kinaba: };
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: // BEGIN CUT HERE
fbe763b30e 2016-05-26        kinaba: #include <ctime>
fbe763b30e 2016-05-26        kinaba: double start_time; string timer()
fbe763b30e 2016-05-26        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
fbe763b30e 2016-05-26        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
fbe763b30e 2016-05-26        kinaba:  { os << "{ ";
fbe763b30e 2016-05-26        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
fbe763b30e 2016-05-26        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
fbe763b30e 2016-05-26        kinaba: void verify_case(const int& Expected, const int& Received) {
fbe763b30e 2016-05-26        kinaba:  bool ok = (Expected == Received);
fbe763b30e 2016-05-26        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
fbe763b30e 2016-05-26        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
fbe763b30e 2016-05-26        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
fbe763b30e 2016-05-26        kinaba: #define END	 verify_case(_, TriangleTriples().count(A, B, C));}
fbe763b30e 2016-05-26        kinaba: int main(){
fbe763b30e 2016-05-26        kinaba: 
fbe763b30e 2016-05-26        kinaba: CASE(0)
fbe763b30e 2016-05-26        kinaba: 	int A = 1;
fbe763b30e 2016-05-26        kinaba: 	int B = 10;
fbe763b30e 2016-05-26        kinaba: 	int C = 20;
fbe763b30e 2016-05-26        kinaba: 	int _ = 10;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: CASE(2)
fbe763b30e 2016-05-26        kinaba: 	int A = 10;
fbe763b30e 2016-05-26        kinaba: 	int B = 10;
fbe763b30e 2016-05-26        kinaba: 	int C = 10;
fbe763b30e 2016-05-26        kinaba: 	int _ = 505;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: CASE(3)
fbe763b30e 2016-05-26        kinaba: 	int A = 1;
fbe763b30e 2016-05-26        kinaba: 	int B = 1;
fbe763b30e 2016-05-26        kinaba: 	int C = 1;
fbe763b30e 2016-05-26        kinaba: 	int _ = 1;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: CASE(1)
fbe763b30e 2016-05-26        kinaba: 	int A = 2;
fbe763b30e 2016-05-26        kinaba: 	int B = 2;
fbe763b30e 2016-05-26        kinaba: 	int C = 1000000000;
fbe763b30e 2016-05-26        kinaba: 	int _ = 6;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: CASE(4)
fbe763b30e 2016-05-26        kinaba: 	int A = 123456789;
fbe763b30e 2016-05-26        kinaba: 	int B = 987654321;
fbe763b30e 2016-05-26        kinaba: 	int C = 555555555;
fbe763b30e 2016-05-26        kinaba: 	int _ = 64296241;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: CASE(4)
fbe763b30e 2016-05-26        kinaba: 	int A = 123456789;
fbe763b30e 2016-05-26        kinaba: 	int B = 555555555;
fbe763b30e 2016-05-26        kinaba: 	int C = 987654321;
fbe763b30e 2016-05-26        kinaba: 	int _ = 64296241;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: CASE(4)
fbe763b30e 2016-05-26        kinaba: 	int A = 555555555;
fbe763b30e 2016-05-26        kinaba: 	int B = 987654321;
fbe763b30e 2016-05-26        kinaba: 	int C = 123456789;
fbe763b30e 2016-05-26        kinaba: 	int _ = 64296241;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: /*
fbe763b30e 2016-05-26        kinaba: CASE(5)
fbe763b30e 2016-05-26        kinaba: 	int A = ;
fbe763b30e 2016-05-26        kinaba: 	int B = ;
fbe763b30e 2016-05-26        kinaba: 	int C = ;
fbe763b30e 2016-05-26        kinaba: 	int _ = ;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: CASE(6)
fbe763b30e 2016-05-26        kinaba: 	int A = ;
fbe763b30e 2016-05-26        kinaba: 	int B = ;
fbe763b30e 2016-05-26        kinaba: 	int C = ;
fbe763b30e 2016-05-26        kinaba: 	int _ = ;
fbe763b30e 2016-05-26        kinaba: END
fbe763b30e 2016-05-26        kinaba: */
fbe763b30e 2016-05-26        kinaba: }
fbe763b30e 2016-05-26        kinaba: // END CUT HERE