EGOI '23 - Find the Box

#include <bits/stdc++.h>

using namespace std;

int main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    int h, w; cin >> h >> w;

    if (h <= 2) { // edge cases
        for (int i = 0; i < h; ++i) {
            cout << "? " << string(i, 'v') + string(w, '>') << endl;
            int r, c; cin >> r >> c;
            if (r != i) {
                cout << "! " << i << " 0" << endl;
                return 0;
            }
            else if (c != w-1) {
                cout << "! " << r << ' ' << c+1 << endl;
                return 0;
            }
        }
    }

    string s;
    for (int i = 0; i < h+1; ++i) s += string(w, '<') + "v" + string(w, '>') + "^>v";
    cout << "? " << s << endl;
    int r, c; cin >> r >> c;
    if (r == h-1 && c == w-1) {
        // either first row or square 1 0
        cout << "? " << ">vv<^^" << string(w, '>') << endl;
        cin >> r >> c;
        if (r == 2) cout << "! 1 0" << endl;
        else cout << "! 0 " << c+1 << endl;
    } else {
        // try first column
        cout << "? " << string(h, 'v') << endl;
        int r2, c2; cin >> r2 >> c2;
        if (r2 != h-1) cout << "! " << r2+1 << " 0" << endl;
        else cout << "! " << r+1 << ' ' << c << endl;
    }
    return 0;
}