We have a sandglass consisting of two bulbs, bulb A and bulb B. These bulbs contain some amount of sand. When we put the sandglass, either bulb A or B lies on top of the other and becomes the upper bulb. The other bulb becomes the lower bulb.

The sand drops from the upper bulb to the lower bulb at a rate of 1 gram per second. When the upper bulb no longer contains any sand, nothing happens.

Initially at time 0, bulb A is the upper bulb and contains a grams of sand; bulb B contains X-a grams of sand (for a total of X grams).

We will turn over the sandglass at time r_1,r_2,..,r_K. Assume that this is an instantaneous action and takes no time. Here, time t refer to the time t seconds after time 0.

You are given Q queries. Each query is in the form of (t_i,a_i). For each query, assume that a=a_i and find the amount of sand that would be contained in bulb A at time t_i.

Constraints

* 1≤X≤10^9
* 1≤K≤10^5
* 1≤r_1<r_2< .. <r_K≤10^9
* 1≤Q≤10^5
* 0≤t_1<t_2< .. <t_Q≤10^9
* 0≤a_i≤X (1≤i≤Q)
* All input values are integers.

Input

The input is given from Standard Input in the following format:


X
K
r_1 r_2 .. r_K
Q
t_1 a_1
t_2 a_2
:
t_Q a_Q


Output

For each query, print the answer in its own line.

Examples

Input

180
3
60 120 180
3
30 90
61 1
180 180


Output

60
1
120


Input

100
1
100000
4
0 100
90 100
100 100
101 100


Output

100
10
0
0


Input

100
5
48 141 231 314 425
7
0 19
50 98
143 30
231 55
342 0
365 100
600 10


Output

19
52
91
10
58
42
100
#include <iostream>
#include <vector>
#include <iomanip>

using namespace std;

class Watch {
public:
	explicit Watch(int X) : X(X), startA(0), curA(0), startB(X), curB(X), up(true) {}
	int query(int time, int a){
		int cur = calcStart_(a) + (up ? -time : time);
		if(cur <= 0) return 0;
		if(cur >= X) return X;
		return cur;
	}
	int progress(int time){
		if(up){
			curA -= time;
			curB -= time;
			if(curB <= 0){
				startA = startB;
				curA = curB = 0;
			} else if(curA <= 0){
				startA -= curA;
				curA = 0;
			}
		} else {
			curA += time;
			curB += time;
			if(curA >= X){
				startB = startA;
				curA = curB = X;
			} else if(curB >= X){
				startB -= curB - X;
				curB = X;
			}
		}
		up = !up;
	}
private:
	int calcStart_(int a){
		if(a <= startA) return curA;
		if(a >= startB) return curB;
		return curA + a - startA;
	}
private:
	const int X;
	int startA, curA, startB, curB;
	bool up;
};

int main(){
	std::ios::sync_with_stdio(false);
	int X, K;
	while(cin >> X >> K){
		vector<int> times;
		times.push_back(0);
		for(int i=0;i<K;i++){
			int a; cin >> a;
			times.push_back(a);
		}
		times.push_back(1000000007);
		Watch watch(X);
		int timeIdx = 0;
		int Q; cin >> Q;
		for(int i=0;i<Q;i++){
			int t, a; cin >> t >> a;
			while(t >= times[timeIdx+1]){
				watch.progress(times[timeIdx+1] - times[timeIdx]);
				++timeIdx;
			}
			cout << watch.query(t - times[timeIdx], a) << endl;
		}
	}
}