Lucky Days

Problem code: LUCKYDAY

All submissions for this problem are available.

Chef Ciel defined a sequence S as follows:
S[1] = A
S[2] = B
S[i] = (X*S[i-1] + Y*S[i-2] + Z) mod P, for i >= 3

Ciel considers C is a lucky number, and the i-th day is a lucky day if and only if S[i] = C. Ciel's restaurant may have special events in a lucky day.

By the way, your work is calculating the numbers of lucky days in intervals. That is, for each Q intervals [L[i], R[i]], you should calculate the number of the integers k which satisfy L[i] <= k <= R[i] and S[k] = C.

Input

The first line contains an integer T, the number of test cases. Then T test cases follow. The first line for each test case has 8 integers A, B, X, Y, Z, P, C and Q. The next Q lines have 2 integers L[i] and R[i].

Output

For each interval, print the number of lucky days in the interval.

Constraints

1 <= T <= 2
2 <= P <= 10007
P is a prime.
0 <= A, B, X, Y, Z, C < P
1 <= Q <= 20000 (2*10^4)
1 <= L[i] <= R[i] <= 1000000000000000000 (10^18)

Sample Input

2
1 1 1 1 0 2 0 6
1 1
2 2
3 3
4 4
5 5
6 6
1 2 4 5 3 17 4 3
5 8
5 58
58 5858

Sample Output

0
0
1
0
0
1
0
4
362

Output details

In the first case:
S[1] = A = 1
S[2] = B = 1
S[3] = (S[2] + S[1]) mod 2 = (1 + 1) mod 2 = 0
S[4] = (S[3] + S[2]) mod 2 = (0 + 1) mod 2 = 1
S[5] = (S[4] + S[3]) mod 2 = (1 + 0) mod 2 = 1
S[6] = (S[5] + S[4]) mod 2 = (1 + 1) mod 2 = 0
S[7] = (S[6] + S[5]) mod 2 = (0 + 1) mod 2 = 1

Author: laycurse
Date Added: 1-10-2011
Time Limit: 5 sec
Source Limit: 50000 Bytes
Languages: ADA, ASM, BASH, BF, C, C99 strict, CAML, CLOJ, CLPS, CPP 4.0.0-8, CPP 4.3.2, CS2, D, ERL, F#, FORT, GO, HASK, ICK, ICON, JAR, JAVA, JS, LISP clisp, LISP sbcl, LUA, NEM, NICE, PAS fpc, PAS gpc, PERL, PERL6, PHP, PIKE, PRLG, PYTH, PYTH 3.1.2, RUBY, SCALA, SCM guile, SCM qobi, ST, TCL, TEXT, WSPC


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