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.
import java.io.*;
import java.util.*;
import java.math.*;
public 
class Main{
    //static variable
    static final int mod = (int) 1e9 + 7;
    static final double eps = 1e-6;
    static final double pi = Math.PI;
    static final long inf = Long.MAX_VALUE / 2;


    // .......static class
  static class Pair{
      int key,value;
      Pair(int key,int value){
        this.key=key;
        this.value=value;
      }
      int Key(){
        return key;
      }
      int Value(){
        return value;
      }
  }
  static class mycomparator implements Comparator<Pair>{
     @Override
     public int compare(Pair o1,Pair o2){
      Integer key1=o1.Key(),key2=o2.Key();
          return key1.compareTo(key2);
     }
  }
    
//.............staic class end.
  
    BufferedReader br;
    PrintWriter out;
    public static void main(String[] args) {
    new Main().main1();
 
  }
  void main1()
  {
    try{
       
        br=new BufferedReader(new InputStreamReader(System.in));
        out=new PrintWriter(System.out);
        int t=1;
       // t=ii();
      while(t-->0){

        //........solution start
        long ns[] = ilong();
        long n = ns[0] , s = ns[1];
        long a[] = ilong();
        long min = getmin(a);
        long sum = 0;
        for(int i=0;i<n;i++){
          sum+=a[i];
        }
        if(sum<s){
          System.out.println("-1");
          continue;
        }
        long ans = findSol(0,min,sum,n,s);
        System.out.println(ans);


      

  
        









        //..........solution end.

     }
     out.flush();
     out.close(); 
    }
    catch(Exception e){
        e.printStackTrace();}    
  }


  // ...............required method.

 long findSol(long l , long r ,long sum,long n , long s){
    long mid = 0;
    long ans = -1;
    while(l<=r){
      mid = l+(r-l)/2;
      long exp = calcExpire(mid,sum,n);
      if(exp >= s){
        ans = Math.max(ans,mid);
        l=mid+1;
      }
      else {
        r=mid-1;
      }
    }
    if(ans<0) ans=0;
    return ans;
  }

  int gcd(int a, int b) { 
    if (a == 0) 
        return b; 
    return gcd(b%a, a); 
  } 
  long calcExpire(long mid , long sum , long n){
    long temp = n*mid;
    return (sum - temp);

  }




  //................end.
  
  
   //..............input method start. 
    int getmax(int a[]){
      int n=a.length;
      int max=a[0];
      for (int i=1;i<n ;i++ ) {
        max=Math.max(a[i],max);
      }
      return max;
    }
     long getmin(long a[]){
      int n=a.length;
      long min=a[0];
      for (int i=1;i<n ;i++ ) {
        min=Math.min(a[i],min);
      }
      return min;
    }

    int[] iint() throws IOException{
      String line[]=br.readLine().split(" ");
      int[] a=new int[line.length];
      for (int i=0;i<line.length ;i++ ) {
        a[i]=Integer.parseInt(line[i]);
      }
      return a;
    }
    long[] ilong() throws IOException{
      String line[]=br.readLine().split(" ");
      long[] a=new long[line.length];
      for (int i=0;i<line.length ;i++ ) {
        a[i]=Long.parseLong(line[i]);
      }
      return a;
    }
    double[] idouble() throws IOException{
      String line[]=br.readLine().split(" ");
      double[] a=new double[line.length];
      for (int i=0;i<line.length ;i++ ) {
        a[i]=Long.parseLong(line[i]);
      }
      return a;
    }
    long li() throws IOException{
      
      return Long.parseLong(br.readLine());
    }
    int ii() throws IOException{
      
      return Integer.parseInt(br.readLine());
    }
    double di() throws IOException{
      return Double.parseDouble(br.readLine());
    }
    char ci() throws IOException{
      return (char)br.read();
    }
    String si() throws IOException{
       return br.readLine();
    }
    String[] isa(int n) throws IOException{
        String at =si();
        return at.split(" ");
    }

    double[][] idm(int n, int m) throws IOException{
        double a[][] = new double[n][m];
        for (int i = 0; i < n; i++) {
          double[] temp=idouble();
          for (int j = 0; j < m; j++) a[i][j] = temp[j];
        }
        return a;
    }

    int[][] iim(int n, int m) throws IOException{
        int a[][] = new int[n][m];
        for (int i = 0; i < n; i++) {
          int[] temp=iint();
          for (int j = 0; j < m; j++) a[i][j] =temp[j];
        }
        return a;
    }
    long[][] ilm(int n, int m) throws IOException{
       long a[][] = new long[n][m];
        for (int i = 0; i < n; i++) {
          long[] temp=ilong();
          for (int j = 0; j < m; j++) a[i][j] =temp[j];
        }
        return a;
    }
    //..............input methods end;
    
} 