Background

Description

Given an array of ints, is it possible to choose a group of some of the ints, such that the group sums to the given target with this additional constraint: If a value in the array is chosen to be in the group, the value immediately following it in the array must not be chosen. (No loops needed.)

Format

Input

Output

Samples

0 [2 5 10 4] 12

true

0 [2 5 10 4] 14

false

0 [2 5 10 4] 7

false

Limitation

1s, 1024KiB for each test case.