The Fair Nut likes kvass very much. On his birthday parents presented him n kegs of kvass. There are v_i liters of kvass in the i-th keg. Each keg has a lever. You can pour your glass by exactly 1 liter pulling this lever. The Fair Nut likes this drink very much, so he wants to pour his glass by s liters of kvass. But he wants to do it, so kvass level in the least keg is as much as possible.

Help him find out how much kvass can be in the least keg or define it's not possible to pour his glass by s liters of kvass.

Input

The first line contains two integers n and s (1 ≤ n ≤ 10^3, 1 ≤ s ≤ 10^{12}) — the number of kegs and glass volume.

The second line contains n integers v_1, v_2, …, v_n (1 ≤ v_i ≤ 10^9) — the volume of i-th keg.

Output

If the Fair Nut cannot pour his glass by s liters of kvass, print -1. Otherwise, print a single integer — how much kvass in the least keg can be.

Examples

Input

3 3
4 3 5


Output

3


Input

3 4
5 3 4


Output

2


Input

3 7
1 2 3


Output

-1

Note

In the first example, the answer is 3, the Fair Nut can take 1 liter from the first keg and 2 liters from the third keg. There are 3 liters of kvass in each keg.

In the second example, the answer is 2, the Fair Nut can take 3 liters from the first keg and 1 liter from the second keg.

In the third example, the Fair Nut can't pour his cup by 7 liters, so the answer is -1.
#_________________ Mukul Mohan Varshney _______________#

#Template
import sys
import os
import math
import copy
from math import gcd
from bisect import bisect
from io import BytesIO, IOBase
from math import sqrt,floor,factorial,gcd,log,ceil
from collections import deque,Counter,defaultdict
from itertools import permutations, combinations

#define function 
def Int(): return int(sys.stdin.readline())
def Mint(): return map(int,sys.stdin.readline().split())
def Lstr(): return list(sys.stdin.readline().strip())
def Str(): return sys.stdin.readline().strip()
def Mstr(): return map(str,sys.stdin.readline().strip().split())
def List(): return list(map(int,sys.stdin.readline().split()))
def Hash(): return dict()
def Mod(): return 1000000007
def Ncr(n,r,p): return ((fact[n])*((ifact[r]*ifact[n-r])%p))%p
def Most_frequent(list): return max(set(list), key = list.count)
def Mat2x2(n): return [List() for _ in range(n)]

def Prime_factors(n):
     i = 2
     factors = set()
     while i * i <= n:
          if n % i:
               i += 1
          else:
               n //= i
               factors.add(i)
     if n > 1:
          factors.add(n)
     print(factors)     
     if len(factors)==2:
          return True
     else:
          return False

def Divisors(n) : 
     l = []  
     for i in range(1, int(math.sqrt(n) + 1)) :
          if (n % i == 0) : 
               if (n // i == i) : 
                    l.append(i) 
               else : 
                    l.append(i)
                    l.append(n//i)
     return l
     
def Sieve(n):                      
     prime=[True for i in range(n+1)]
     lst=[]
     p=2
     while p*p<=n:
          if prime[p]:
               for i in range(p*p,n+1,p):
                    prime[i]=False
          p=p+1
     for i in range(2,n+1):
          if prime[i]:
               lst.append(i)
     return lst    
     
def minimum_integer_not_in_list(a):
     b=max(a)
     if(b<1):
          return 1
          
     A=set(a)
     B=set(range(1,b+1))
     D=B-A
     if len(D)==0:
          return b+1
     else:
          return min(D)
 
# Driver Code 	
def solution():
     n,s=Mint()
     a=List()
     if(sum(a)<s):
          print(-1)
     else:
          print(min(min(a),(sum(a)-s)//n))

#Call the solve function          
if __name__ == "__main__":
     solution()  