923_B. Producing Snow
Alice likes snow a lot! Unfortunately, this year's winter is already over, and she can't expect to have any more of it. Bob has thus bought her a gift — a large snow maker. He plans to make some amount of snow every day. On day i he will make a pile of snow of volume Vi and put it in her garden.

Each day, every pile will shrink a little due to melting. More precisely, when the temperature on a given day is Ti, each pile will reduce its volume by Ti. If this would reduce the volume of a pile to or below zero, it disappears forever. All snow piles are independent of each other. 

Note that the pile made on day i already loses part of its volume on the same day. In an extreme case, this may mean that there are no piles left at the end of a particular day.

You are given the initial pile sizes and the temperature on each day. Determine the total volume of snow melted on each day. 

Input

The first line contains a single integer N (1 ≤ N ≤ 105) — the number of days. 

The second line contains N integers V1, V2, ..., VN (0 ≤ Vi ≤ 109), where Vi is the initial size of a snow pile made on the day i.

The third line contains N integers T1, T2, ..., TN (0 ≤ Ti ≤ 109), where Ti is the temperature on the day i.

Output

Output a single line with N integers, where the i-th integer represents the total volume of snow melted on day i.

Examples

Input

3
10 10 5
5 7 2


Output

5 12 4


Input

5
30 25 20 15 10
9 10 12 4 13


Output

9 20 35 11 25

Note

In the first sample, Bob first makes a snow pile of volume 10, which melts to the size of 5 on the same day. On the second day, he makes another pile of size 10. Since it is a bit warmer than the day before, the first pile disappears completely while the second pile shrinks to 3. At the end of the second day, he has only a single pile of size 3. On the third day he makes a smaller pile than usual, but as the temperature dropped too, both piles survive till the end of the day.
```python
n=int(input())
v=list(map(int,input().split()))
t=list(map(int,input().split()))

sumv=list()
sumv.append(0)
for i in range(n):
    sumv.append(sumv[i]+v[i])
sumt=list()
sumt.append(0)
for i in range(n):
    sumt.append(sumt[i]+t[i])

ans=[0]*(n)
add=[0]*(n+1)
for i in range(n):
    if(v[i]<=t[i]):
        ans[i]+=v[i]
    elif(v[i]>=sumt[n]-sumt[i]):
        add[i]+=1
    else:
        l=i+1;r=n;mid=(r+l)//2
        while (r>l):
            mid=(r+l)//2
            if (sumt[mid]-sumt[i]==v[i]):
                r=mid
                break
            elif(sumt[mid]-sumt[i]>v[i]):
                r=mid
            else:
                l=mid+1
        ans[r-1]+=(v[i]-sumt[r-1]+sumt[i])
        add[i]+=1;add[r-1]-=1

tmpcnt=0
for i in range(n):
    tmpcnt+=add[i]
    ans[i]+=(tmpcnt*t[i])

print(' '.join( i for i in map(str,ans)))
 		  	 			 			       			 		  		
```