SUBSUMS - Subset Sums


Given a sequence of N (1 ≤ N ≤ 34) numbers S1, ..., SN (-20,000,000 ≤ Si ≤ 20,000,000), determine how many subsets of S (including the empty one) have a sum between A and B (-500,000,000 ≤ A ≤ B ≤ 500,000,000), inclusive.

Input

The first line of standard input contains the three integers N, A, and B. The following N lines contain S1 through SN, in order.

Output

Print a single integer to standard output representing the number of subsets satisfying the above property. Note that the answer may overflow a 32-bit integer.

Example

Input:
3 -1 2
1
-2
3

Output:
5

The following 5 subsets have a sum between -1 and 2:

  • 0 = 0 (the empty subset)
  • 1 = 1
  • 1 + (-2) = -1
  • -2 + 3 = 1
  • 1 + (-2) + 3 = 2

hide comments
mahak_rawat: 2021-04-05 17:33:21

Getting wrong answer in 14th test case. Can anyone help?

aviral_tiwari: 2021-02-18 12:05:10

Take Care of duplicates in array....Use lower and upper bound accordingly..

reaped_juggler: 2021-02-14 09:48:53

Be Careful on the condition while applying STL :) cost me 3 WA

nil_s: 2021-02-13 13:57:39

Getting WA on 14th testcase . Anybody can help??

hackerbhaiya: 2021-01-02 16:07:01

starter of meet in the middle algorithm :)

daddys_home: 2020-12-28 16:39:53

learn meet in the middle coz of this problem.
https://www.geeksforgeeks.org/meet-in-the-middle/

matias222: 2020-08-24 06:21:29

Finally after 1 week of trying AC, it is a meet in the middle problem, just focus on doing a right bs

goa_baba: 2020-06-16 21:04:11

very poor test cases!
does it considers only distinct subsets?
for eg if arr->(1,2,2)
does it consider -> {},{1},{2},{1,2},{1,2,2},{2,2}
or -> {},{1},{2},{2},{1,2},{1,2},{2,2},{1,2,2}?
I was considering the later case & getting wrong answer on the last test case

bhati_r45: 2020-05-16 07:27:20

the first 14 test cases are very weak and finally got ac

scolar_fuad: 2019-12-20 07:43:44

my first meet in the middle dp ... bitmask + binary search ...
happy coding


Added by:Neal Wu
Date:2009-01-19
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO