为什么下面的代码会抛出 std::bad_alloc

我已经编写了代码来测试两个数组中存在多少个相同的数字，但由于某种原因，它抛出"std：：bad_alloc"谁能解释为什么？由于某种原因，它仅在N = 1000000时抛出它，是因为我分配了4000000字节的内存吗？

代码如下：

#include <iostream>
#include <vector>
#include <string>
#include <random>
#include <algorithm>
#include <math.h>
#include <iomanip>
using namespace std;
int find_last_before_zero(const vector<int>& vec) {
 for (int i = vec.size() - 1; i >= 0; --i) {
    if (vec[i] != 0) return i + 1;
 }
return vec.size();
}
void gen_random_array(vector<int>& vec){
random_device rd;
mt19937 gen(rd());
uniform_int_distribution<> dist(100000, 100200);
for(int i = 0; i < vec.size(); ++i){
    vec[i] = dist(gen);
}
}
void binSearchClient(int T){
int counters[4] = {0,0,0,0};
string names[4] = {"for n = 1000 = ", "for n = 10000 = ", "for n = 100000 = ", "for n = 1000000 = "};
for(int i = 0; i < T; ++i){
    int N = 1000;
    for(int k = 0; k < 4; ++k){
        N *= pow(10.0, k);
        vector<int> first(N), second(N);
        gen_random_array(first, N); gen_random_array(second, N);
        vector<int> intersection(N);
        sort(first.begin(), first.end()); sort(second.begin(), second.end());
        set_intersection(first.begin(), first.end(), second.begin(), second.end(), intersection.begin());
        counters[k] += find_last_before_zero(intersection);
            }
        }
    }
}
for(int i = 0; i < 4; ++i){
    cout << names[i] << setprecision(10) << std::fixed << (1.0 * counters[i]) / T << endl;
}
}
int main(){
binSearchClient(1);
}