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<bits/stdc++.h>

using namespace std;

const int N=100010;
int r[N],tup[N],tdn[N];
int n,X;
int q;
int a,t;
int s[N];

int getlw(int p){
    int L=0,R=n;
    while(L<R){
	//cout<<L<<' '<<R<<endl;
	int mid=(L+R+1)>>1;
	if(r[mid]>p)R=mid-1;
	else{
	    L=mid;
	}
    }
    return L;
}

int main()
{
    //freopen("c.in","r",stdin);
    //freopen("c.out","w",stdout);
    scanf("%d",&X);
    tup[0]=X;
    scanf("%d",&n);
    for(int i=1;i<=n;i++){
	scanf("%d",&r[i]);
	if(i%2){
	    s[i]=s[i-1]-r[i]+r[i-1];
	    tup[i]=tup[i-1]-r[i]+r[i-1];
	    tdn[i]=tdn[i-1]-r[i]+r[i-1];
	}
	else{
	    s[i]=s[i-1]+r[i]-r[i-1];
	    tup[i]=tup[i-1]+r[i]-r[i-1];
	    tdn[i]=tdn[i-1]+r[i]-r[i-1];
	}
	if(tup[i]>X)tup[i]=X;
	else if(tup[i]<0)tup[i]=0;
	if(tdn[i]>X)tdn[i]=X;
	else if(tdn[i]<0)tdn[i]=0;
	//cout<<tup[i]<<' '<<tdn[i]<<endl;
    }
    scanf("%d",&q);
    while(q--)
    {
	scanf("%d%d",&t,&a);
	int p=getlw(t);
	//cout<<p<<endl;
	int up,dn,now;
	if((p+1)%2){
	    up=tup[p]-t+r[p];
	    dn=tdn[p]-t+r[p];
	    now=s[p]-t+r[p];
	}else{
            up=tup[p]+t-r[p];
	    dn=tdn[p]+t-r[p];
	    now=s[p]+t-r[p];
	}
	now+=a;
	if(up>X)up=X;
	else if(up<0)up=0;
	if(dn>X)dn=X;
	else if(dn<0)dn=0;
	//cout<<up<<'|'<<now<<'|'<<dn<<endl;
	if(now>up)now=up;
	if(now<dn)now=dn;
	printf("%d\n",now);
    }
}

