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// Cryptoconference
// Solution by 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 <unordered_map>
#include <unordered_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); }
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<PR> S;
// returns the # of valid intervals with start positions in:
// (this interval's start, next interval's start]
LL Count(set<PR>::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<PR>::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);
} |