Odd Binomial CoefficientsProblem code: ODDBIN |
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If P(x) is a polynomial in x with integer coefficients, let W(P(x)) = number of odd coefficients of P(x).
Given a1, a2, ... , am, find W( (1+x)a1 + (1+x)a2 + ... + (1+x)am ).
Input
First line contains TC, the number of test cases.
Each test case consists of a single line in the format:
m a1 a2 ... am
Limits
1 <= m <= 15
0 <= ai < 260
1 <= TC <= 1000
Output
Output one line per test case, the value W( (1+x)a1 + (1+x)a2 + ... + (1+x)am ).
Example
Input:
4
1 1
1 3
2 1 3
3 1 2 3
Output:
2
4
2
2
Explanation
(1+x) + (1+x)3 = 2 + 4x + 3x2 + x3. Hence the output for "2 1 3" is 2. (2 odd coefficients)
(1+x) + (1+x)2 + (1+x)3 = 3 + 6x + 4x2 + x3. Hence the output for "3 1 2 3" is 2.
| Author: | subra |
| Date Added: | 15-10-2010 |
| Time Limit: | 7 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, TEXT, WSPC |
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