Why this code in C++ doesn't work?

vector<vector<int> > v(4);

vector<int> k(4,0);

for (int i=0; i<v.size(); i++)
    v.push_back(k);

for (int i=0; i<v.size(); i++) {
    for (int j=0; j<k.size(); j++)
        cout << v[i][j];
    cout << endl;

I think it should work but the program doesn't execute anything. Where am I wrong?