Sandglass

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

inputFormat

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

outputFormat

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

样例

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

19
52
91
10
58
42
100

</p>