What is wrong with my equivalent code from vector<bool> to bitset

Question

I was solving this problem on HackerRanked and found the following solution:

#include <iostream>
#include <vector>
using namespace std;
int main() {
    constexpr size_t BIG = 1u<<31;
    vector<bool> arr(BIG);
    size_t N,S,P,Q;
    cin >> N >> S >> P >> Q;
    size_t prev = S % BIG;
    arr.at(prev) = true;
    int count = 0;
    while (N--) {
        size_t curr = (prev*P+Q)% BIG;
        if(!arr.at(curr))
        {
            arr.at(curr) = true;
            ++count;
        }
        prev = curr;
    }
    cout << count;
}

I wanted to solve the same question using bitset, however it is not working... What am I doing wrong here?

#include <iostream>
#include <bitset>
using namespace std;
int main() {
    constexpr size_t BIG = 1u<<31;
    bitset<BIG> arr;
    size_t N, S, P, Q;
    cin >> N >> S >> P >> Q;
    size_t prev = S % BIG;
    arr.set(prev);
    while (N--) {
        size_t curr = (prev*P+Q)% BIG;
        arr.set(curr); prev = curr;
    }
    cout << arr.count();
}