Problem p02685 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long int
using namespace __gnu_pbds;
typedef tree<pair<ll, pair<ll, ll>>, null_type, less<pair<ll, pair<ll, ll>>>,
             rb_tree_tag, tree_order_statistics_node_update>
    ordered_set;
#define me BOSS
#define bug() cout << "AIkahne aise" << endl
#define PI acos(-1)
/* Precode Start Here *\\
     Sieve
void sieve()
{
    for(ll i=3; i<=2000; i+=2)
    {
        for(ll j=i*i; j<=4000000; j+=i)
            A[j]=1;
    }
    v.push_back(2);
    for(ll i=3; i<=4000000; i+=2)
        if(A[i]==0)
            v.push_back(i);
}

     Power Function Modulo P

ll modPow(ll a, ll x, ll p) {
    //calculates a^x mod p in logarithmic time.
    long res = 1;
    while(x > 0) {
        if( x % 2 != 0) {
            res = (res * a) % p;
        }
        a = (a * a) % p;
        x /= 2;
    }
    return res;
}


   factorial

ll fact(ll n)
{
    ll ans=1;
    for(ll i=1;i<=n;i++)
    {
        ans=(ans*i)%mod;
    }
    return ans;
}
     Calculating nCr using Fermats law Theorem

ll modInverse(ll a, ll p) {
    //calculates the modular multiplicative of a mod m.
    //(assuming p is prime).
    return modPow(a, p-2, p);
}


ll modBinomial(ll n, ll k, ll p) {
// calculates C(n,k) mod p (assuming p is prime).

    ll numerator = 1; // n * (n-1) * ... * (n-k+1)
    for (ll i=0; i<k; i++) {
        numerator = (numerator * (n-i) ) % p;
    }

    ll denominator = 1; // k!
    for (ll i=1; i<=k; i++) {
        denominator = (denominator * i) % p;
    }

    // numerator / denominator mod p.
    return ( numerator* modInverse(denominator,p) ) % p;
}
     num of divisor and euler totient

ll phi[1000001],mark[1000001],divi[1000001];;
void divisorPhi(ll n)
{
    for(int i=1;i<=n;i++)
        phi[i]=i;
    for(int i=2;i<=n;i++)
    {
        if(!mark[i])
        {
            for(int j=i;j<=n;j+=i)
            {
                mark[j]=1;
                phi[j]*=(1-1/(double)i);
            }
        }
    }
    for(ll i=1;i<=n;i++)
    {
        for(ll j=i;j<=n;j+=i)
            divi[j]++;
    }
}
/* Precode Ends */
#define mod 998244353
ll fact[5000001], B[5000001];
vector<ll> v;
map<ll, ll> myMap;
set<ll> mySet;
vector<pair<ll, ll>> vp;
priority_queue<ll> pq;
priority_queue<ll, vector<ll>, std::greater<ll>> first;
ll po(ll a, ll n) {
  ll ans = 1;
  for (int i = 1; i <= n; i++)
    ans *= a;
  return ans;
}

ll modPow(ll a, ll x, ll p) {
  // calculates a^x mod p in logarithmic time.
  long res = 1;
  while (x > 0) {
    if (x % 2 != 0) {
      res = (res * a) % p;
    }
    a = (a * a) % p;
    x /= 2;
  }
  return res;
}

ll modInverse(ll a, ll p) {
  // calculates the modular multiplicative of a mod m.
  //(assuming p is prime).
  return modPow(a, p - 2, p);
}

ll modBinomial(ll n, ll k, ll p) {
  return fact[n] * modInverse((fact[k] * fact[n - k]) % mod, mod);
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  ll n, m, k, ans = 0, t;
  fact[0] = 1;
  cin >> n >> m >> k;
  for (int i = 1; i <= n; i++) {
    fact[i] = (i * fact[i - 1]) % mod;
    fact[i] %= mod;
  }
  for (int i = n - k - 1; i < n; i++) {
    t = modBinomial(n - 1, i, mod);
    t %= mod;
    t *= m;
    t %= mod;
    t *= modPow(m - 1, i, mod);
    t %= mod;
    ans += t;
    ans %= mod;
  }
  cout << ans << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long int
using namespace __gnu_pbds;
typedef tree<pair<ll, pair<ll, ll>>, null_type, less<pair<ll, pair<ll, ll>>>,
             rb_tree_tag, tree_order_statistics_node_update>
    ordered_set;
#define me BOSS
#define bug() cout << "AIkahne aise" << endl
#define PI acos(-1)
/* Precode Start Here *\\
     Sieve
void sieve()
{
    for(ll i=3; i<=2000; i+=2)
    {
        for(ll j=i*i; j<=4000000; j+=i)
            A[j]=1;
    }
    v.push_back(2);
    for(ll i=3; i<=4000000; i+=2)
        if(A[i]==0)
            v.push_back(i);
}

     Power Function Modulo P

ll modPow(ll a, ll x, ll p) {
    //calculates a^x mod p in logarithmic time.
    long res = 1;
    while(x > 0) {
        if( x % 2 != 0) {
            res = (res * a) % p;
        }
        a = (a * a) % p;
        x /= 2;
    }
    return res;
}


   factorial

ll fact(ll n)
{
    ll ans=1;
    for(ll i=1;i<=n;i++)
    {
        ans=(ans*i)%mod;
    }
    return ans;
}
     Calculating nCr using Fermats law Theorem

ll modInverse(ll a, ll p) {
    //calculates the modular multiplicative of a mod m.
    //(assuming p is prime).
    return modPow(a, p-2, p);
}


ll modBinomial(ll n, ll k, ll p) {
// calculates C(n,k) mod p (assuming p is prime).

    ll numerator = 1; // n * (n-1) * ... * (n-k+1)
    for (ll i=0; i<k; i++) {
        numerator = (numerator * (n-i) ) % p;
    }

    ll denominator = 1; // k!
    for (ll i=1; i<=k; i++) {
        denominator = (denominator * i) % p;
    }

    // numerator / denominator mod p.
    return ( numerator* modInverse(denominator,p) ) % p;
}
     num of divisor and euler totient

ll phi[1000001],mark[1000001],divi[1000001];;
void divisorPhi(ll n)
{
    for(int i=1;i<=n;i++)
        phi[i]=i;
    for(int i=2;i<=n;i++)
    {
        if(!mark[i])
        {
            for(int j=i;j<=n;j+=i)
            {
                mark[j]=1;
                phi[j]*=(1-1/(double)i);
            }
        }
    }
    for(ll i=1;i<=n;i++)
    {
        for(ll j=i;j<=n;j+=i)
            divi[j]++;
    }
}
/* Precode Ends */
#define mod 998244353
ll A[5000001], B[5000001];
vector<ll> v;
map<ll, ll> myMap;
set<ll> mySet;
vector<pair<ll, ll>> vp;
priority_queue<ll> pq;
priority_queue<ll, vector<ll>, std::greater<ll>> first;
ll po(ll a, ll n) {
  ll ans = 1;
  for (int i = 1; i <= n; i++)
    ans *= a;
  return ans;
}

ll modPow(ll a, ll x, ll p) {
  // calculates a^x mod p in logarithmic time.
  long res = 1;
  while (x > 0) {
    if (x % 2 != 0) {
      res = (res * a) % p;
    }
    a = (a * a) % p;
    x /= 2;
  }
  return res;
}

ll modInverse(ll a, ll p) {
  // calculates the modular multiplicative of a mod m.
  //(assuming p is prime).
  return modPow(a, p - 2, p);
}

ll modBinomial(ll n, ll k, ll p) {
  // calculates C(n,k) mod p (assuming p is prime).

  ll numerator = 1; // n * (n-1) * ... * (n-k+1)
  for (ll i = 0; i < k; i++) {
    numerator = (numerator * (n - i)) % p;
  }

  ll denominator = 1; // k!
  for (ll i = 1; i <= k; i++) {
    denominator = (denominator * i) % p;
  }

  // numerator / denominator mod p.
  return (numerator * modInverse(denominator, p)) % p;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  ll n, m, k, ans = 0, t;
  cin >> n >> m >> k;
  for (int i = n - k - 1; i < n; i++) {
    t = modBinomial(n - 1, i, mod);
    t %= mod;
    t *= m;
    t %= mod;
    t *= modPow(m - 1, i, mod);
    t %= mod;
    ans += t;
    ans %= mod;
  }
  cout << ans << endl;
  return 0;
}