Counting inversions in C++ via mergesort - c++

Question

I have a text file that contains 100,000 numbers from 1 ~ 100,000 in an unsorted manner (no duplicates).
The name of the file is "IntegerArray.txt"
My task is to count the number of inversions in the text file. An inversion is a pair of elements a, b where a comes before b, but a > b. Thus "1 2 3 6 4 5" contains two inversion (6 > 4 and 6 > 5).
I implemented it with the merge sorting method; the sorting works, but the counting inversions part kept giving out wrong answers, and I cannot find why.
The following is my code:
long long mergeAndCount(vector<int>& vec, int p, int q, int r) {
long long count = 0;
vector<int> L, R;
for (int i = p; i <= q; ++i) L.push_back(vec[i]);
for (int j = q + 1; j <= r; ++j) R.push_back(vec[j]);
L.push_back(numeric_limits<int>::max()); //sentinel element
R.push_back(numeric_limits<int>::max());
int i = 0, j = 0;
for (int k = p; k <= r; ++k) {
if (L[i] <= R[j]) {
vec[k] = L[i];
++i;
} else {
vec[k] = R[j];
++j;
if (L[i] != L.back() && R[j] != R.back())
// Problem SOLVED: change this line to count += q - p + 1 - i
count += q - i + 1;
}
}
return count;
}
long long inversion(vector<int>& vec, int p, int r) {
long long count = 0;
if (p < r) {
int q = (p + r) / 2;
count = inversion(vec, p, q);
count += inversion(vec, q + 1, r);
count += mergeAndCount(vec, p, q, r);
}
return count;
}
int main() {
ifstream infile("IntegerArray.txt");
int a;
vector<int> vec;
while (infile >> a)
vec.push_back(a);
cout << inversion(vec, 0, vec.size()-1);
return 0;
}
The result from the above code is 32620796130, which is incorrect.
The answer by brute force with the following code is 2407905288, which is correct.
long long inversion(vector<int>& vec, int p, int r) {
long long count = 0;
for (int i = 0; i < vec.size(); ++i)
for (int j = i + 1; j < vec.size(); ++j)
if (vec[i] > vec[j])
++count;
return count;
}
Can someone help me out solving this?