Codeforces 745 div 2 problem B solution.cpp

#include<bits/stdc++.h>
using namespace std;
#define endl "\n" /*for interactive problems remove this line*/
/*
-for ordered set problems policy based data sucture header
//PBDS

*/ 



typedef  long long  ll;
ll mod = pow(10, 9) + 7;
typedef unsigned long long  ull;
int gcdExtended(int a, int b, int *x, int *y);
 
// Function to find modulo inverse of b. It returns
// -1 when inverse doesn't
int modInverse(int b, int m)
{
  int x, y; // used in extended GCD algorithm
  int g = gcdExtended(b, m, &x, &y);
 
  // Return -1 if b and m are not co-prime
  if (g != 1)
    return -1;
 
  // m is added to handle negative x
  return (x % m + m) % m;
}
int gcdExtended(int a, int b, int *x, int *y)
{
  // Base Case
  if (a == 0)
  {
    *x = 0, *y = 1;
    return b;
  }
 
  int x1, y1; // To store results of recursive call
  int gcd = gcdExtended(b % a, a, &x1, &y1);
 
  // Update x and y using results of recursive
  // call
  *x = y1 - (b / a) * x1;
  *y = x1;
 
  return gcd;
}
 
ll sumbincoef( int N, int k ) {
  ll   bincoef = 1, sum = 1;
  int i;
  for ( i = 1 ; i < k ; i++ ) {
    ll val=((N - i + 1)%mod *modInverse( i,mod))%mod;
    bincoef = (bincoef%mod * val)%mod;
    if(i%2==0)
    sum = (sum+bincoef)%mod;
  }
  return sum%mod;
}
 
const int N = 200000 + 10;
ll factorialNumInverse[N + 1];
 
// aay to precompute inverse of 1! to N!
ll naturalNumInverse[N + 1];
 
// aay to store factorial of first N numbers
ll fact[N + 1];
 
// Function to precompute inverse of numbers
void InverseofNumber(ll p)
{
  naturalNumInverse[0] = naturalNumInverse[1] = 1;
  for (int i = 2; i <= N; i++)
    naturalNumInverse[i] = naturalNumInverse[p % i] * (p - p / i) % p;
}
// Function to precompute inverse of factorials
void InverseofFactorial(ll p)
{
  factorialNumInverse[0] = factorialNumInverse[1] = 1;
 
  // precompute inverse of natural numbers
  for (int i = 2; i <= N; i++)
    factorialNumInverse[i] = (naturalNumInverse[i] * factorialNumInverse[i - 1]) % p;
}
 
// Function to calculate factorial of 1 to N
void factorial(ll p)
{
  fact[0] = 1;
 
  // precompute factorials
  for (int i = 1; i <= N; i++) {
    fact[i] = (fact[i - 1] * i) % p;
  }
}
 
// Function to return nCr % p in O(1) time
ll Binomial(ll N, ll R, ll p)
{
  // n C r = n!*inverse(r!)*inverse((n-r)!)
  ll ans = ((fact[N] * factorialNumInverse[R])
            % p * factorialNumInverse[N - R])
           % p;
  return ans;
}
 
 
 
typedef unsigned long long  ull;
 
typedef unsigned int ui;
/*IMP snippets
 //PBDS -for ordered set problems policy based data sucture header
//binaryToDecimal
//decimalToBinary
//nCrModp
 
//is_prime
 
//segtree*/
  
int parent[N],ran[N];
void make_set(int v) {
    parent[v] = v;
    ran[v]=0;
}
int find_set(int v) {
    if (v == parent[v])
        return v;
    return parent[v]=find_set(parent[v]);
}
void union_sets(int a, int b) {
    a = find_set(a);
    b = find_set(b);
    if (a != b){
      if(ran[a]<ran[b])swap(a,b);
      parent[b] = a;
      if(ran[a]==ran[b])ran[a]++;
    }
  }
  




int main()
{ ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL);
  mt19937 rng((unsigned int) chrono::steady_clock::now().time_since_epoch().count());
 
#ifndef ONLINE_JUDGE
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
#endif
  
  ll p=mod;
  InverseofNumber(p);
  InverseofFactorial(p);
  factorial(p);
 


 int t=1;
 cin>>t;
 while(t>0)
 {
   ll n,m,k;
   cin>>n>>m>>k;
   if(m<n-1||m>n*(n-1)/2)
   {
    cout<<"NO"<<endl;
   }
   else
   {  
     if(n==1)
     { if(k>=2)
       cout<<"YES"<<endl;
       else 
       {
        cout<<"NO"<<endl;
       }
     }
     else if(k>=4)
     {
    cout<<"YES"<<endl;
     }
     else if(k==0)
     {
      cout<<"NO"<<endl; 
     }
     else if(k==1)
     {
      cout<<"NO"<<endl;
     }
     else if(k==2)
     {
      cout<<"NO"<<endl;
     }
     else if(k==3)
     {
        if(m==n*(n-1)/2)
        {
          cout<<"YES"<<endl;
        }
        else
        {
          cout<<"NO"<<endl;
        }
     }
   }


     


  t--;
 }  
   




}