SEQ - Recursive Sequence
Sequence (ai) of natural numbers is defined as follows:
ai = bi (for i <= k)
ai = c1ai-1 + c2ai-2 + ... + ckai-k (for i > k)
where bj and cj are given natural numbers for 1<=j<=k. Your task is to compute an for given n and output it modulo 109.
Input
On the first row there is the number C of test cases (equal to about 1000).
Each test contains four lines:
k - number of elements of (c) and (b) (1 <= k <= 10)
b1,...,bk - k natural numbers where 0 <= bj <= 109 separated by spaces
c1,...,ck - k natural numbers where 0 <= cj <= 109 separated by spaces
n - natural number (1 <= n <= 109)
Output
Exactly C lines, one for each test case: an modulo 109
Example
Input: 3 3 5 8 2 32 54 6 2 3 1 2 3 4 5 6 6 3 24 354 6 56 57 465 98765432 Output: 8 714 257599514
hide comments
aruneshg:
2017-12-26 16:41:57
when to take mod
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amulyagaur:
2017-08-30 20:26:50
ac in 1 go |
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babur:
2017-08-22 19:43:16
How can output of 3rd case be 257599514, this number is greater than 1e9 and so by modulo the output must be 57599514. Where am I going please help.. |
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Rajat Sharma:
2016-08-06 13:56:12
Java: will learn matrix exponentiation with recursion, linear recursive equations, how to solve these equations by converting the addition into multiplicative expressions i.e. through matrices.
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Deepak Singh Tomar:
2016-03-07 15:56:45
matrix_exponentiation. Thanks fushar :) |
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minhthai:
2016-02-03 17:26:12
be careful the mod is 10^9 not 10^9 + 7 :) |
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Ðức Tân:
2015-08-27 18:45:42
dễ vãi |
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r0bo_dart:
2015-06-25 07:28:24
Hint: While doing matrix multiplication, DON'T do temp[][] += mod(F[][] * M[][]);
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sHaShAnK sHeKhAr:
2015-06-21 18:23:23
Nice problem to reach 150 :)
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i_am_looser:
2015-05-30 15:59:01
learnt something new.......... ; ) |
Added by: | Paweł Dobrzycki |
Date: | 2005-04-29 |
Time limit: | 0.5s-3s |
Source limit: | 8196B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All |
Resource: | IV Podlasian Contest in Team Programming |