# Interactive LowerBound

This is an interactive problem.

You are given a sorted in increasing order singly linked list. You should find the minimum integer in the list which is greater than or equal to x.

More formally, there is a singly liked list built on an array of n elements. Element with index i contains two integers: value i is the integer value in this element, and next i that is the index of the next element of the singly linked list (or -1, if the current element is the last). The list is sorted, i.e. if next i ≠  - 1, then value next i > value i.

You are given the number of elements in the list n, the index of the first element start, and the integer x.

You can make up to 2000 queries of the following two types:

• ? i (1 ≤ i ≤ n) — ask the values value i and next i,
• ! ans — give the answer for the problem: the minimum integer, greater than or equal to x, or ! -1, if there are no such integers. Your program should terminate after this query.

Write a program that solves this problem.

Input

The first line contains three integers nstartx (1 ≤ n ≤ 50000, 1 ≤ start ≤ n, 0 ≤ x ≤ 109) — the number of elements in the list, the index of the first element and the integer x.

Output

To print the answer for the problem, print ! ans, where ans is the minimum integer in the list greater than or equal to x, or -1, if there is no such integer.Interaction

To make a query of the first type, print ? i (1 ≤ i ≤ n), where i is the index of element you want to know information about.

After each query of type ? read two integers value i and next i (0 ≤ value i ≤ 109,  - 1 ≤ next i ≤ nnext i ≠ 0).

It is guaranteed that if next i ≠  - 1, then value next i > value i, and that the array values give a valid singly linked list with start being the first element.

Note that you can’t ask more than 1999 queries of the type ?.

If next i =  - 1 and value i =  - 1, then it means that you asked more queries than allowed, or asked an invalid query. Your program should immediately terminate (for example, by calling exit(0)). You will receive “Wrong Answer”, it means that you asked more queries than allowed, or asked an invalid query. If you ignore this, you can get other verdicts since your program will continue to read from a closed stream.

Your solution will get “Idleness Limit Exceeded”, if you don’t print anything or forget to flush the output, including the final answer.

To flush you can use (just after printing a query and line end):

• fflush(stdout) in C++;
• System.out.flush() in Java;
• stdout.flush() in Python;
• flush(output) in Pascal;
• For other languages see documentation.

Hacks format

For hacks, use the following format:

In the first line print three integers nstartx (1 ≤ n ≤ 50000, 1 ≤ start ≤ n, 0 ≤ x ≤ 109).

In the next n lines print the description of the elements of the list: in the i-th line print two integers value i and next i (0 ≤ value i ≤ 109,  - 1 ≤ next i ≤ nnext i ≠ 0).

The printed structure should be a valid singly linked list. In particular, it should be possible to reach all elements from start by following links next i, and the last element end should have -1 in the next end.

Example

input

5 3 8097 -158 516 281 179 4

output

? 1? 2? 3? 4? 5! 81

Note

The illustration for the first sample case. Start and finish elements are marked dark.

Solution:

#include <bits/stdc++.h>

using namespace std;

inline pair <int, int> ask(int id) {
printf("? %d\n", id);
fflush(stdout);
pair <int, int> p;
scanf("%d %d", &p.first, &p.second);
return p;
}

inline void finish(int value) {
printf("! %d\n", value);
fflush(stdout);
exit(0);
}

inline int RAND(int n) {
return abs((rand() << 15) + rand()) % n;
}

const int MAGIC = 1000;

int main() {
int n, start, x;
scanf("%d %d %d", &n, &start, &x);
srand(time(0));
set <int> all;
all.insert(start);
while ((int) all.size() < min(n, MAGIC)) {
all.insert(RAND(n) + 1);
}
vector < pair <int, int> > v;
for (int i : all) {
pair <int, int> z = ask(i);
v.emplace_back(z.first, i);
}
sort(v.begin(), v.end());
int ptr = start;
for (int i = 0; i < (int) v.size(); i++) {
if (v[i].first < x) {
ptr = v[i].second;
}
}
while (ptr != -1) {
pair <int, int> z = ask(ptr);
if (z.first >= x) {
finish(z.first);
return 0;
}
ptr = z.second;
}
finish(-1);
return 0;
}