F. Power Tower

Codeforces

IDCF904F

Time4000ms

Memory256MB

Difficulty—

mathnumber theory

Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the current top of tower and adding rocks at its bottom. If top, which is built from _k_ - 1 rocks, possesses power _p_ and we want to add the rock charged with power _w__k_ then value of power of a new tower will be {_w__k_}_p_. Rocks are added from the last to the first. That is for sequence _w_1, ..., _w__m_ value of power will be After tower is built, its power may be extremely large. But still priests want to get some information about it, namely they want to know a number called cumulative power which is the true value of power taken modulo _m_. Priests have _n_ rocks numbered from 1 to _n_. They ask you to calculate which value of cumulative power will the tower possess if they will build it from rocks numbered _l_, _l_ + 1, ..., _r_. ## Input First line of input contains two integers _n_ (1 ≤ _n_ ≤ 105) and _m_ (1 ≤ _m_ ≤ 109). Second line of input contains _n_ integers _w__k_ (1 ≤ _w__k_ ≤ 109) which is the power of rocks that priests have. Third line of input contains single integer _q_ (1 ≤ _q_ ≤ 105) which is amount of queries from priests to you. _k__th_ of next _q_ lines contains two integers _l__k_ and _r__k_ (1 ≤ _l__k_ ≤ _r__k_ ≤ _n_). ## Output Output _q_ integers. _k_\-th of them must be the amount of cumulative power the tower will have if is built from rocks _l__k_, _l__k_ + 1, ..., _r__k_. [samples] ## Note 327 = 7625597484987

Samples

Input #1

6 1000000000
1 2 2 3 3 3
8
1 1
1 6
2 2
2 3
2 4
4 4
4 5
4 6

Output #1

API Response (JSON)

{
  "problem": {
    "name": "F. Power Tower",
    "description": {
      "content": "Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the curren",
      "description_type": "Markdown"
    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "CF904F"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Priests of the Quetzalcoatl cult want to build a tower to represent a power of their god. Tower is usually made of power-charged rocks. It is built with the help of rare magic by levitating the curren...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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