p02354 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.

Examples

Input

6 4
1 2 1 2 3 2


Output

2


Input

6 6
1 2 1 2 3 2


Output

3


Input

3 7
1 2 3


Output

0
```python
#import pysnooper
#import numpy
#import os,re,sys,operator
#from collections import Counter,deque
#from operator import itemgetter
#from itertools import accumulate,combinations,groupby,combinations_with_replacement,permutations
from sys import stdin,setrecursionlimit
from bisect import bisect_left
#from copy import deepcopy
#import heapq
#import math
#import string

setrecursionlimit(10**6)
input=stdin.readline

n,s=map(int,input().split())
a=[int(i) for i in input().split()]
nows=0
ans=2<<20
left=0
for right in range(n):
    nows+=a[right]
    while left<=right and right<n:
        if nows>=s:
            ans=min(ans,right-left+1)
            nows-=a[left]
            left+=1
        else: break
        #print(nows)
print(ans%(2<<20))

```