// Cryptoconference // Solution by Jacob Plachta #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; #define LL long long #define LD long double #define PR pair #define Fox(i,n) for (i=0; 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 T Abs(T x) { return(x < 0 ? -x : x); } template T Sqr(T x) { return(x * x); } string plural(string s) { return(Sz(s) && s[Sz(s) - 1] == 'x' ? s + "en" : s + "s"); } const int INF = (int)1e9; const LD EPS = 1e-12; const LD PI = acos(-1.0); #define GETCHAR getchar_unlocked 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 int N, K; LL cur, ans; set S; // returns the # of valid intervals with start positions in: // (this interval's start, next interval's start] LL Count(set::iterator I) { // get key points from this interval and the next one int a = I->x + 1; I++; int b = I->x; int c = I->y - 1; // count intervals which start in [a, b] and end no later than c int v1 = c - b; int v2 = c - a; return (LL)(v1 + v2) * (v2 - v1 + 1) / 2; } // inserts interval [a, b] into the set, while updating the total # of valid intervals void Insert(int a, int b) { set::iterator I, J; I = S.lower_bound(mp(a, -1)); // is the new interval obsolete (covers existing interval)? if (a <= I->x && I->y <= b) return; // erase any existing obsolete intervals (covering the new one) if (I->x > a) I--; for (;;) { if (I->y < b) break; J = I, I--; cur -= Count(J) + Count(I); S.erase(J); cur += Count(I); } // insert the new interval cur -= Count(I); S.insert(mp(a, b)); cur += Count(I); I++; cur += Count(I); } LL ProcessCase() { int i; // input Read(N), Read(K); // init S.clear(); S.insert(mp(-1, -1)); S.insert(mp(K, K + 1)); ans = 1; cur = Count(S.begin()); // process intervals Fox(i, N) { int s, d; Read(s), Read(d); Insert(s, s + d); ans = ans * (cur % MOD) % MOD; } return(ans); } int main() { int T, t; Read(T); Fox1(t, T) printf("Case #%d: %lld\n", t, ProcessCase()); return(0); }