Skittles

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

const int MOD = 998244353;
const int MAX = 200010;

ll power_mod(ll x, ll y, ll mod) {
    ll res = 1;
    x %= mod;
    while(y > 0){
        if(y & 1){
            res = res * x % mod;
        }
        x = x * x % mod;
        y >>=1;
    }
    return res;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    ll n, a, b;
    cin >> n >> a >> b;
    
    if(n ==1){
        if(a > b){
            cout << 0;
        }
        else{
            ll result = (b - a +1) % MOD;
            cout << result;
        }
        return 0;
    }
    
    ll max_val = n + b;
    vector<ll> fact(max_val +1, 1);
    for(int i=1;i<=max_val;i++) {
        fact[i] = fact[i-1] * i % MOD;
    }
    vector<ll> inv_fact(max_val +1,1);
    inv_fact[max_val] = power_mod(fact[max_val], MOD -2, MOD);
    for(int i=max_val -1;i>=0;i--){
        inv_fact[i] = inv_fact[i+1] * (i+1) % MOD;
    }
    
    auto comb = [&](ll k) -> ll {
        ll N = n + k -1;
        ll K = n -1;
        if(N < K || K <0) return 0;
        return fact[N] * inv_fact[K] % MOD * inv_fact[N - K] % MOD;
    };
    
    ll result =0;
    for(ll k =a; k <= b; k++){
        result = (result + comb(k)) % MOD;
    }
    cout << result;
}

Test 1

Verdict: ACCEPTED

Test 2

Verdict: ACCEPTED

Test 3

Verdict: ACCEPTED

Test 4

Verdict: ACCEPTED

Test 5

Verdict: ACCEPTED

Test 6

Verdict: ACCEPTED

Test 7

Verdict: ACCEPTED

Test 8

Verdict: ACCEPTED

Test 9

Verdict: ACCEPTED

Test 10

Verdict: ACCEPTED

Test 11

Verdict: ACCEPTED

Test 12

Verdict: ACCEPTED

Test 13

Verdict: ACCEPTED

Test 14

Verdict: ACCEPTED

Test 15

Verdict: ACCEPTED

Test 16

Verdict: ACCEPTED

Test 17

Verdict: ACCEPTED

Test 18

Verdict: ACCEPTED

Test 19

Verdict: ACCEPTED

Test 20

Verdict: ACCEPTED

Test 21

Verdict: ACCEPTED

Test 22

Verdict: ACCEPTED

Test 23

Verdict: ACCEPTED

Test 24

Verdict: ACCEPTED

Test 25

Verdict: ACCEPTED

Test 26

Verdict: ACCEPTED

Test 27

Verdict: ACCEPTED

Test 28

Verdict: ACCEPTED

Test 29

Verdict: ACCEPTED

Test 30

Verdict: ACCEPTED

Test 31

Verdict: ACCEPTED

Test 32

Verdict: ACCEPTED

Test 33

Verdict: ACCEPTED

Test 34

Verdict: ACCEPTED

Test 35

Verdict: ACCEPTED

Test 36

Verdict: ACCEPTED

Test 37

Verdict: ACCEPTED

Test 38

Verdict: ACCEPTED

Test 39

Verdict: ACCEPTED

Test 40

Verdict: ACCEPTED

Test 41

Verdict: ACCEPTED

Test 42

Verdict: ACCEPTED

Test 43

Verdict: ACCEPTED

Test 44

Verdict: ACCEPTED

Test 45

Verdict: ACCEPTED

Test 46

Verdict: ACCEPTED

Test 47

Verdict: ACCEPTED

Test 48

Verdict: ACCEPTED

Test 49

Verdict: ACCEPTED

Test 50

Verdict: ACCEPTED

Test 51

Verdict: ACCEPTED

Test 52

Verdict: ACCEPTED

Test 53

Verdict: ACCEPTED

Test 54

Verdict: ACCEPTED

Test 55

Verdict: ACCEPTED

Test 56

Verdict: ACCEPTED

Test 57

Verdict: ACCEPTED

Test 58

Verdict: ACCEPTED

Test 59

Verdict: ACCEPTED

Test 60

Verdict: ACCEPTED

Test 61

Verdict: ACCEPTED

Test 62

Verdict: ACCEPTED

Test 63

Verdict: ACCEPTED