Problem:
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The Smallest Window I

For a given array $a_1, a_2, a_3, ... , a_N$ of $N$ elements and an integer $S$, find the smallest sub-array size (smallest window length) where the sum of the sub-array is greater than or equal to $S$. If there is not such sub-array, report 0.

Constraints

$1 \leq N \leq 10^5$

$1 \leq S \leq 10^9$

$1 \leq a_i \leq 10^4$

Input

The input is given in the following format.

$N$ $S$

$a_1$ $a_2$ ... $a_N$

Output

Print the smallest sub-array size in a line.

Sample Input 1

6 4
1 2 1 2 3 2

Sample Output 1

2

Sample Input 2

6 6
1 2 1 2 3 2

Sample Output 2

3

Sample Input 3

3 7
1 2 3

Sample Output 3

0

Solution in Haskell (judge verdict: Memory Limit Exceeded)

import Control.Applicative
import Data.List
import Data.Maybe

main = do
  [n,s] <- map read.words<$>getLine
  list <- map read.words<$>getLine
  print $ solve s list

solve :: Int -> [Int] -> Int
solve s list = if sum list < s then 0
                          else foldr f' maxBound.filter' s.foldr ((++).inits) [].tails $ list

f' a b = b `min` length a

filter' :: Int -> [[Int]] -> [[Int]]
filter' s = foldr (\x xs -> if sum x >= s then x:xs else xs) []