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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class C {

    public static void main(String[] args) throws IOException {
        ReaderC.init(System.in);
        int n = ReaderC.nextInt();
        long[] v = new long[n];
        long[] t = new long[n];
        for (int i = 0; i < v.length; i++) v[i] = ReaderC.nextLong();
        for (int i = 0; i < t.length; i++) t[i] = ReaderC.nextLong();

        long[] prefixT = new long[t.length];
        prefixT[0] = t[0];
        for (int i = 1; i < prefixT.length; i++) prefixT[i] = prefixT[i - 1] + t[i];

        int[] repeat = new int[n];
        long[] additional = new long[n];

        for (int i = 0; i < v.length; i++) {
            long search = 0;
            if (i > 0) search = prefixT[i - 1];
            search += v[i];
            int index = lowerBound(prefixT, prefixT.length, search);
//            System.out.println(index);
            repeat[i]++;

            if (index < prefixT.length) {
                repeat[index]--;
//                additional[index] = v[i] - (index > 0 ? prefixT[index - 1] - (i > 0 ? prefixT[i - 1] : 0) : 0);
                additional[index] += search - (index > 0 ? prefixT[index - 1] : 0);
            }
        }

        long[] ans = new long[n];
        for (int i = 0; i < repeat.length; i++) {
            if (i > 0) repeat[i] += repeat[i - 1];
        }

        for (int i = 0; i < ans.length; i++) ans[i] = t[i]*repeat[i] + additional[i];
//        System.out.println(Arrays.toString(additional));
        System.out.println(Arrays.toString(ans).replace(", ", " ").replace("[", "").replace("]", ""));
    }

    private static int lowerBound(long[] array, int length, long value) {
        int low = 0;
        int high = length;
        while (low < high) {
            final int mid = (low + high) / 2;
            if (value <= array[mid]) {
                high = mid;
            } else {
                low = mid + 1;
            }
        }
        return low;
    }
}

/**
 * Reader class based on the article at "https://www.cpe.ku.ac.th/~jim/java-io.html"
 */
class ReaderC {
    private static BufferedReader reader;
    private static StringTokenizer tokenizer;

    static void init(InputStream inputStream) {
        reader = new BufferedReader(new InputStreamReader(inputStream));
        tokenizer = new StringTokenizer("");
    }

    private static String next() throws IOException {
        String read;
        while (!tokenizer.hasMoreTokens()) {
            read = reader.readLine();
            if (read == null || read.equals(""))
                return "-1";
            tokenizer = new StringTokenizer(read);
        }

        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

//    //    Get a whole line.
//    static String line() throws IOException {
//        return reader.readLine();
//    }
//
//    static double nextDouble() throws IOException {
//        return Double.parseDouble(next());
//    }
}

