Sandglass

AtCoder

IDarc082_d

Time2000ms

Memory256MB

Difficulty—

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: $X$ $K$ $r_1$ $r_2$ .. $r_K$ $Q$ $t_1$ $a_1$ $t_2$ $a_2$ $:$ $t_Q$ $a_Q$ [samples]

Samples

Input #1

Output #1

60
1
120

In the first query, $30$ out of the initial $90$ grams of sand will drop from bulb A, resulting in $60$ grams. In the second query, the initial $1$ gram of sand will drop from bulb A, and nothing will happen for the next $59$ seconds. Then, we will turn over the sandglass, and $1$ second after this, bulb $A$ contains $1$ gram of sand at the time in question.

Input #2

Output #2

100
10
0
0

In every query, the upper bulb initially contains $100$ grams, and the question in time comes before we turn over the sandglass.

Input #3

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

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Sandglass",
    "description": {
      "content": "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 _upp",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc082_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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 _upp...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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