Visit of the Great

3000ms

262144K

Description:

The Great Mushroom King descended to the dwarves, but not everyone managed to see him. Only the few chosen ones could see the King.

We know that only LCM(k^{2^l} + 1, k^{2^l + 1} + 1, ..., k^{2^r} + 1) dwarves can see the Great Mushroom King. Numbers k, l, r are chosen by the Great Mushroom King himself in some complicated manner which is unclear to common dwarves.

The dwarven historians decided to document all visits of the Great Mushroom King. For each visit the dwarven historians know three integers k_i, l_i, r_i, chosen by the Great Mushroom King for this visit. They also know a prime number p_i. Help them to count the remainder of dividing the number of dwarves who can see the King, by number p_i, for each visit.

Input:

The first line contains the single integer t (1 ≤ t ≤ 10⁵) — the number of the King's visits.

Each of the following t input lines contains four space-separated integers k_i, l_i, r_i and p_i (1 ≤ k_i ≤ 10⁶; 0 ≤ l_i ≤ r_i ≤ 10¹⁸; 2 ≤ p_i ≤ 10⁹) — the numbers, chosen by the Great Mushroom King and the prime module, correspondingly.

It is guaranteed that for all visits number p_i is prime.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output:

For each visit print the answer on a single line — the remainder of dividing the number of the dwarves who can see the King this time, by number p_i. Print the answers for the visits in the order, in which the visits are described in the input.

Sample Input:

2
3 1 10 2
5 0 4 3

Sample Output:

0
0

Note:

We consider that LCM(a₁, a₂, ..., a_n) represents the least common multiple of numbers a₁, a₂, ..., a_n.

We consider that x⁰ = 1, for any x.

Informação

Provedor Codeforces

Código CF185D