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<cstdio>
#include<algorithm>
using namespace std;
const int M = 100100;
int x, k, r[M], q, ans[M];
struct Query {
	int t, a, id;
}qry[M * 2];

bool cmp(Query a, Query b) {
	return a.t < b.t;
}

int main() {
	scanf("%d%d", &x, &k);
	for(int i = 1; i <= k; i++) {
		scanf("%d", &qry[i].t);
		qry[i].id = 0;
	}
	scanf("%d", &q);
	for(int i = 1; i <= q; i++) {
		scanf("%d%d", &qry[i + k].t, &qry[i + k].a);
		qry[i + k].id = i;
	}
	sort(qry + 1, qry + q + k + 1, cmp);
	int j = 1;
	int a = 0, a_len = 1, b = x, cge = -1;
	for(int i = 1; i <= q + k; i++) {
		int cp = qry[i].t - qry[i - 1].t;
		if(cge == -1) {
			if(cp > a) {
				a_len += cp - a;
				a = 0;
				
			} else a -= cp;
			b -= cp;
			if(a_len > x + 1) a_len = x + 1;
			if(b < 0) b = 0, a_len = x + 1;
			if(a < 0) a = 0;
		} else {
			a += cp;
			b += cp;
			if(b > x) b = x;
			if(a > x) a = x, a_len = x + 1;
		}
		if(qry[i].id == 0) cge = -cge; 
		else {
			//
			if(qry[i].a < a_len) ans[qry[i].id] = a;
			else if(qry[i].a < a_len + b - a) ans[qry[i].id] = qry[i].a - a_len + a + 1;
			else ans[qry[i].id] = b;
		}//printf("%d %d %d\n", a, a_len, b);
	}
	for(int i = 1; i <= q; i++) printf("%d\n", ans[i]);
	return 0;
}