6828085ccd 2015-09-11        kinaba: #include <iostream>
6828085ccd 2015-09-11        kinaba: #include <sstream>
6828085ccd 2015-09-11        kinaba: #include <iomanip>
6828085ccd 2015-09-11        kinaba: #include <vector>
6828085ccd 2015-09-11        kinaba: #include <string>
6828085ccd 2015-09-11        kinaba: #include <map>
6828085ccd 2015-09-11        kinaba: #include <set>
6828085ccd 2015-09-11        kinaba: #include <algorithm>
6828085ccd 2015-09-11        kinaba: #include <numeric>
6828085ccd 2015-09-11        kinaba: #include <iterator>
6828085ccd 2015-09-11        kinaba: #include <functional>
6828085ccd 2015-09-11        kinaba: #include <complex>
6828085ccd 2015-09-11        kinaba: #include <queue>
6828085ccd 2015-09-11        kinaba: #include <stack>
6828085ccd 2015-09-11        kinaba: #include <cmath>
6828085ccd 2015-09-11        kinaba: #include <cassert>
6828085ccd 2015-09-11        kinaba: #include <tuple>
6828085ccd 2015-09-11        kinaba: using namespace std;
6828085ccd 2015-09-11        kinaba: typedef long long LL;
6828085ccd 2015-09-11        kinaba: typedef complex<double> CMP;
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: static const unsigned MODVAL = 1000000007;
6828085ccd 2015-09-11        kinaba: struct mint
6828085ccd 2015-09-11        kinaba: {
6828085ccd 2015-09-11        kinaba: 	unsigned val;
6828085ccd 2015-09-11        kinaba: 	mint():val(0){}
6828085ccd 2015-09-11        kinaba: 	mint(int      x):val(x%MODVAL) {}
6828085ccd 2015-09-11        kinaba: 	mint(unsigned x):val(x%MODVAL) {}
6828085ccd 2015-09-11        kinaba: 	mint(LL       x):val(x%MODVAL) {}
6828085ccd 2015-09-11        kinaba: };
6828085ccd 2015-09-11        kinaba: mint& operator+=(mint& x, mint y) { return x = x.val+y.val; }
6828085ccd 2015-09-11        kinaba: mint& operator-=(mint& x, mint y) { return x = x.val-y.val+MODVAL; }
6828085ccd 2015-09-11        kinaba: mint& operator*=(mint& x, mint y) { return x = LL(x.val)*y.val; }
6828085ccd 2015-09-11        kinaba: mint operator+(mint x, mint y) { return x+=y; }
6828085ccd 2015-09-11        kinaba: mint operator-(mint x, mint y) { return x-=y; }
6828085ccd 2015-09-11        kinaba: mint operator*(mint x, mint y) { return x*=y; }
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: class CountBinarySequences { public:
6828085ccd 2015-09-11        kinaba: 	int countSequences(int n, int k, vector <int> L, vector <int> R)
6828085ccd 2015-09-11        kinaba: 	{
6828085ccd 2015-09-11        kinaba: 		const int N = L.size();
6828085ccd 2015-09-11        kinaba: 		vector<pair<int,int>> RNG;
6828085ccd 2015-09-11        kinaba: 		for(int i=0; i<N; ++i)
6828085ccd 2015-09-11        kinaba: 			RNG.emplace_back(L[i], R[i]);
6828085ccd 2015-09-11        kinaba: 		sort(RNG.begin(), RNG.end(), [&](pair<int,int> a, pair<int,int> b){
6828085ccd 2015-09-11        kinaba: 			if(a.second-a.first != b.second-b.first)
6828085ccd 2015-09-11        kinaba: 				return a.second-a.first < b.second-b.first;
6828085ccd 2015-09-11        kinaba: 			return a<b;
6828085ccd 2015-09-11        kinaba: 		});
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: 		vector<vector<int>> child(N+1);
6828085ccd 2015-09-11        kinaba: 		for(int i=0; i<N; ++i) {
6828085ccd 2015-09-11        kinaba: 			int p = N;
6828085ccd 2015-09-11        kinaba: 			for(int k=i+1; k<N; ++k)
6828085ccd 2015-09-11        kinaba: 				if(RNG[k].first<=RNG[i].first && RNG[i].second<=RNG[k].second)
6828085ccd 2015-09-11        kinaba: 					{p=k; break;}
6828085ccd 2015-09-11        kinaba: 			child[p].emplace_back(i);
6828085ccd 2015-09-11        kinaba: 		}
6828085ccd 2015-09-11        kinaba: 		for(auto& cc: child)
6828085ccd 2015-09-11        kinaba: 			sort(cc.begin(), cc.end(), [&](int a, int b){
6828085ccd 2015-09-11        kinaba: 				return RNG[a].first < RNG[b].first;
6828085ccd 2015-09-11        kinaba: 			});
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: 		RNG.emplace_back(1, n);
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: 		memo.assign((N+1)*(k+1)*(k+1), -1);
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: 		mint total = 0;
6828085ccd 2015-09-11        kinaba: 		for(int l=0; l<=k; ++l)
6828085ccd 2015-09-11        kinaba: 		for(int r=0; r<=k; ++r)
6828085ccd 2015-09-11        kinaba: 			total += solve(RNG, child, k, N, l, r);
6828085ccd 2015-09-11        kinaba: 		return total.val;
6828085ccd 2015-09-11        kinaba: 	}
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: 	vector<int> memo;
6828085ccd 2015-09-11        kinaba: 	int solve(
6828085ccd 2015-09-11        kinaba: 		const vector<pair<int,int>>& RNG,
6828085ccd 2015-09-11        kinaba: 		const vector<vector<int>>& rng_list,
6828085ccd 2015-09-11        kinaba: 		const int K,
6828085ccd 2015-09-11        kinaba: 		int idx, int L1, int R1) {
6828085ccd 2015-09-11        kinaba: 		const bool must_be_even = (idx+1 == RNG.size());
6828085ccd 2015-09-11        kinaba: 		const int key = (idx*(K+1)+L1)*(K+1)+R1;
6828085ccd 2015-09-11        kinaba: 		if(memo[key] != -1) return memo[key];
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: 		// RNG[idx] is the current range you need to consider.
6828085ccd 2015-09-11        kinaba: 		// rng_list[idx] is left-to-right sorted sub-ranges.
6828085ccd 2015-09-11        kinaba: 		// the region must be sum-even if must_be_even.
6828085ccd 2015-09-11        kinaba: 		// more than K consecutive 1's are not allowed.
6828085ccd 2015-09-11        kinaba: 		// left-end must have exactly L1 consecutive 1's.
6828085ccd 2015-09-11        kinaba: 		// right-end must have exactly R1 consecutive 1's.
6828085ccd 2015-09-11        kinaba: 		return memo[key] = 0;
6828085ccd 2015-09-11        kinaba: 	}
6828085ccd 2015-09-11        kinaba: };
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: // BEGIN CUT HERE
6828085ccd 2015-09-11        kinaba: #include <ctime>
6828085ccd 2015-09-11        kinaba: double start_time; string timer()
6828085ccd 2015-09-11        kinaba:  { ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
6828085ccd 2015-09-11        kinaba: template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
6828085ccd 2015-09-11        kinaba:  { os << "{ ";
6828085ccd 2015-09-11        kinaba:    for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
6828085ccd 2015-09-11        kinaba:    os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
6828085ccd 2015-09-11        kinaba: void verify_case(const int& Expected, const int& Received) {
6828085ccd 2015-09-11        kinaba:  bool ok = (Expected == Received);
6828085ccd 2015-09-11        kinaba:  if(ok) cerr << "PASSED" << timer() << endl;  else { cerr << "FAILED" << timer() << endl;
6828085ccd 2015-09-11        kinaba:  cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
6828085ccd 2015-09-11        kinaba: #define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
6828085ccd 2015-09-11        kinaba: #define END	 verify_case(_, CountBinarySequences().countSequences(n, k, L, R));}
6828085ccd 2015-09-11        kinaba: int main(){
6828085ccd 2015-09-11        kinaba: 
6828085ccd 2015-09-11        kinaba: CASE(0)
6828085ccd 2015-09-11        kinaba: 	int n = 4;
6828085ccd 2015-09-11        kinaba: 	int k = 2;
6828085ccd 2015-09-11        kinaba: 	int L_[] = {2};
6828085ccd 2015-09-11        kinaba: 	  vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
6828085ccd 2015-09-11        kinaba: 	int R_[] = {3};
6828085ccd 2015-09-11        kinaba: 	  vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
6828085ccd 2015-09-11        kinaba: 	int _ = 5;
6828085ccd 2015-09-11        kinaba: END
6828085ccd 2015-09-11        kinaba: CASE(1)
6828085ccd 2015-09-11        kinaba: 	int n = 4;
6828085ccd 2015-09-11        kinaba: 	int k = 1;
6828085ccd 2015-09-11        kinaba: 	int L_[] = {2};
6828085ccd 2015-09-11        kinaba: 	  vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
6828085ccd 2015-09-11        kinaba: 	int R_[] = {2};
6828085ccd 2015-09-11        kinaba: 	  vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
6828085ccd 2015-09-11        kinaba: 	int _ = 6;
6828085ccd 2015-09-11        kinaba: END
6828085ccd 2015-09-11        kinaba: CASE(2)
6828085ccd 2015-09-11        kinaba: 	int n = 6;
6828085ccd 2015-09-11        kinaba: 	int k = 3;
6828085ccd 2015-09-11        kinaba: 	int L_[] = {1, 2, 3};
6828085ccd 2015-09-11        kinaba: 	  vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
6828085ccd 2015-09-11        kinaba: 	int R_[] = {6, 5, 4};
6828085ccd 2015-09-11        kinaba: 	  vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
6828085ccd 2015-09-11        kinaba: 	int _ = 6;
6828085ccd 2015-09-11        kinaba: END
6828085ccd 2015-09-11        kinaba: CASE(3)
6828085ccd 2015-09-11        kinaba: 	int n = 1000;
6828085ccd 2015-09-11        kinaba: 	int k = 4;
6828085ccd 2015-09-11        kinaba: 	int L_[] = {10, 101, 201, 110, 121};
6828085ccd 2015-09-11        kinaba: 	  vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
6828085ccd 2015-09-11        kinaba: 	int R_[] = {100, 200, 300, 120, 130};
6828085ccd 2015-09-11        kinaba: 	  vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
6828085ccd 2015-09-11        kinaba: 	int _ = 444743885;
6828085ccd 2015-09-11        kinaba: END
6828085ccd 2015-09-11        kinaba: CASE(4)
6828085ccd 2015-09-11        kinaba: 	int n = 1;
6828085ccd 2015-09-11        kinaba: 	int k = 5;
6828085ccd 2015-09-11        kinaba: 	int L_[] = {1};
6828085ccd 2015-09-11        kinaba: 	  vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
6828085ccd 2015-09-11        kinaba: 	int R_[] = {1};
6828085ccd 2015-09-11        kinaba: 	  vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
6828085ccd 2015-09-11        kinaba: 	int _ = 1;
6828085ccd 2015-09-11        kinaba: END
6828085ccd 2015-09-11        kinaba: CASE(5)
6828085ccd 2015-09-11        kinaba: 	int n = 998;
6828085ccd 2015-09-11        kinaba: 	int k = 2;
6828085ccd 2015-09-11        kinaba: 	int L_[] = {313,365,189,913,334,360,160,931,313,402,389,328,376,47,906,383,381,927,338,178,934,933,162,332,191,188,380,912,970,360,161,179,966,405,971,381};
6828085ccd 2015-09-11        kinaba: 	  vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
6828085ccd 2015-09-11        kinaba: 	int R_[] = {313,365,189,913,334,362,160,931,340,405,389,329,398,425,907,383,382,927,338,178,934,933,162,332,191,188,384,912,970,365,161,179,966,405,971,381};
6828085ccd 2015-09-11        kinaba: 	  vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
6828085ccd 2015-09-11        kinaba: 	int _ = 420889003;
6828085ccd 2015-09-11        kinaba: END
6828085ccd 2015-09-11        kinaba: /*
6828085ccd 2015-09-11        kinaba: CASE(6)
6828085ccd 2015-09-11        kinaba: 	int n = ;
6828085ccd 2015-09-11        kinaba: 	int k = ;
6828085ccd 2015-09-11        kinaba: 	int L_[] = ;
6828085ccd 2015-09-11        kinaba: 	  vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
6828085ccd 2015-09-11        kinaba: 	int R_[] = ;
6828085ccd 2015-09-11        kinaba: 	  vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
6828085ccd 2015-09-11        kinaba: 	int _ = ;
6828085ccd 2015-09-11        kinaba: END
6828085ccd 2015-09-11        kinaba: CASE(7)
6828085ccd 2015-09-11        kinaba: 	int n = ;
6828085ccd 2015-09-11        kinaba: 	int k = ;
6828085ccd 2015-09-11        kinaba: 	int L_[] = ;
6828085ccd 2015-09-11        kinaba: 	  vector <int> L(L_, L_+sizeof(L_)/sizeof(*L_));
6828085ccd 2015-09-11        kinaba: 	int R_[] = ;
6828085ccd 2015-09-11        kinaba: 	  vector <int> R(R_, R_+sizeof(R_)/sizeof(*R_));
6828085ccd 2015-09-11        kinaba: 	int _ = ;
6828085ccd 2015-09-11        kinaba: END
6828085ccd 2015-09-11        kinaba: */
6828085ccd 2015-09-11        kinaba: }
6828085ccd 2015-09-11        kinaba: // END CUT HERE