rdbuf() strange behavior

I'm trying to merge two files into one by simply using rdbuf(), but when merged, the file's first line is missing. The code is below:

void mergeFiles(ifstream &file1, ifstream &file2, ofstream &file3) {

    int num1;
    int num2;

    string firstLine_1;
    string firstLine_2;

    getline(file1, firstLine_1);
    num1 = atoi(firstLine_1.c_str());

    getline(file2, firstLine_2);
    num2 = atoi(firstLine_2.c_str());

    if (num1<num2) {
        file3 << file1.rdbuf() << "\n" << file2.rdbuf();
    } else {
        file3 << file2.rdbuf() << "\n" << file1.rdbuf();
    }
}