Codeforces Round #350 (Div. 2)_D2 - Magic Powder - 2

D2. Magic Powder - 2

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

The term of this problem is the same as the previous one, the only exception — increased restrictions.

Input

The first line contains two positive integers n and k (1 ≤ n ≤ 100 000, 1 ≤ k ≤ 109) — the number of ingredients and the number of grams of the magic powder.

The second line contains the sequence a1, a2, ..., an (1 ≤ ai ≤ 109), where the i-th number is equal to the number of grams of the i-th ingredient, needed to bake one cookie.

The third line contains the sequence b1, b2, ..., bn (1 ≤ bi ≤ 109), where the i-th number is equal to the number of grams of the i-th ingredient, which Apollinaria has.

Output

Print the maximum number of cookies, which Apollinaria will be able to bake using the ingredients that she has and the magic powder.

Examples

input

1 1000000000
1
1000000000

output

2000000000

input

10 1
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
1 1 1 1 1 1 1 1 1 1

output

0

input

3 1
2 1 4
11 3 16

output

4

input

4 3
4 3 5 6
11 12 14 20

output

3

题解：二分答案的经典应用

 #include<cstdio>
 #define LL long long
 #define FFC(i,a,b) for(int i=a;i<=b;i++)
 LL a[],b[],n,k,maxn=*1e9+;
 void fre(){freopen("c:\\acm\\input.txt","r",stdin);}
 LL search(LL l,LL r){
     LL mid,sum;
     while(l<=r){
         mid=(l+r)>>,sum=;
         FFC(i,,n){
             sum+=a[i]*mid-b[i]>?a[i]*mid-b[i]:;
             if(sum>k)break;//防爆LL
         }
         if(sum==k)return mid;
         else if(sum<k)l=mid+;
         else r=mid-;
     }
     return r;
 }
 int main(){
     //fre();
     while(~scanf("%I64d%I64d",&n,&k)){
         FFC(i,,n)scanf("%I64d",&a[i]);
         FFC(i,,n)scanf("%I64d",&b[i]);
         printf("%I64d\n",search(,maxn));
     }
     return ;
 }