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Print All Paths With Target Sum Subset

1. You are given a number n, representing the count of elements. 2. You are given n numbers. 3. You are given a number "tar". 4. You are required to calculate and print true or false, if there is a subset the elements of which add up to "tar" or not. 5. Also, you have to print the indices of elements that should be selected to achieve the given target. 6. You have to print all such configurations.

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Print All Paths With Target Sum Subset

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1. You are given a number n, representing the count of elements. 2. You are given n numbers. 3. You are given a number "tar". 4. You are required to calculate and print true or false, if there is a subset the elements of which add up to "tar" or not. 5. Also, you have to print the indices of elements that should be selected to achieve the given target. 6. You have to print all such configurations.

Constraints

1 <= n <= 30 0 <= n1, n2, .. n elements <= 20 0 <= tar <= 50

Format

Input

A number n n1 n2 .. n number of elements A number tar

Output

Check the sample output and question video.

Example

Sample Input

5 4 2 7 1 3 10

Sample Output

true 2 4 1 2 3 0 1 3 4

Question Video

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