1. Problem 1:

   You are given scales for weighing loads. On the left side lies a single stone of known weight W < 2N . You own a set of N different weights, weighing 1, 2, 4, ..., 2^N−1 units of mass respectively. Determine how many possible ways there are of placing some weights on the sides of the scales, so as to balance them (put them in a state of equilibrium).
   
   

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   Input Specification
   The input line contains two integers: N W, where N denotes the number of weights and W represents the weight to be placed on the left side.
   
   

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   Output Specification
   Output must be a single integer denoting the number ways in which one can balance the weight W by placing weights on any side
   
   

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   Sample Input and Output
   Input: 2 4
   Output: 3
   Input: 5 10
   Output: 14
   

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2. Problem 2:

   Given a weighing pan, n weights and a destination weight D, print “YES� or “NO� depending whether you can weight D using other weights given.
   
   

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   Input Specification
   Input begins with numbers of weights n, then n values denoting mass of each weight and then in the end destination weight D.

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   Output Specification
   As the output, print “YES� if it is possible to weight D, otherwise “NO�

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   Sample Input and Output
   Input: 3 1 3 4 2
   Output: YES
   Input: 2 1 3 5
   Output: NO