Passing vector by reference: Segmentation fault

I'm trying to get the following code for merge sort work with vectors instead of C style arrays and I'm having a hard time figuring out why it crashes with segmentation fault. Can someone help me out in understanding the problem here?

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

void merge(vector<int>& a, int l, int m, int r) {
    vector<int> L;
    vector<int> R;

    for (int i = 0; i <= m; i++)
        L.push_back(a[i]);
    for (int i = m+1; i <= r; i++)
        R.push_back(a[i]);

    int i = 0, j = 0; // Initial index of first and second subarray
    int k = l;  // Initial index of merged subarray
    while (i < L.size() && j < R.size()) {
        if (L[i] <= R[j]) {
            a[k] = L[i];
            i++;
        }
        else {
            a[k] = R[j];
            j++;
        }
        k++;
    }

    // Filling leftovers
    while (i < L.size()) {
        a[k] = L[i];
        k++;
        i++;
    }
    while (j < R.size()) {
        a[k] = R[j];
        k++;
        j++;
    }
}

void merge_sort(vector<int>& a, int l, int r) {
    if (l < r) {
        int m = l + (r-l) / 2; // Avoids integer overflow.
        merge_sort(a, l, m);
        merge_sort(a, m+1, r);
        merge(a, l, m, r);
    }
}

int main()
{
    vector<int> a = {2, 4, 1, 5, 3, 9};
    int size = a.size();    
    merge_sort(a, 0, size-1);
    for (int i = 0; i < size; i++)
        cout << a[i] << ' ';
    cout << endl;
    return 0;
}