2020/finals/cryptoconference.cpp

// 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);
}