There are n cities in the country where the Old Peykan lives. These cities are located on a straight line, we'll denote them from left to right as c1, c2, ..., cn. The Old Peykan wants to travel from city c1 to cn using roads. There are (n - 1) one way roads, the i-th road goes from city ci to city ci + 1 and is di kilometers long.

The Old Peykan travels 1 kilometer in 1 hour and consumes 1 liter of fuel during this time.

Each city ci (except for the last city cn) has a supply of si liters of fuel which immediately transfers to the Old Peykan if it passes the city or stays in it. This supply refreshes instantly k hours after it transfers. The Old Peykan can stay in a city for a while and fill its fuel tank many times. 

Initially (at time zero) the Old Peykan is at city c1 and s1 liters of fuel is transferred to it's empty tank from c1's supply. The Old Peykan's fuel tank capacity is unlimited. Old Peykan can not continue its travel if its tank is emptied strictly between two cities.

Find the minimum time the Old Peykan needs to reach city cn.

Input

The first line of the input contains two space-separated integers m and k (1 ≤ m, k ≤ 1000). The value m specifies the number of roads between cities which is equal to n - 1.

The next line contains m space-separated integers d1, d2, ..., dm (1 ≤ di ≤ 1000) and the following line contains m space-separated integers s1, s2, ..., sm (1 ≤ si ≤ 1000).

Output

In the only line of the output print a single integer — the minimum time required for The Old Peykan to reach city cn from city c1.

Examples

Input

4 6
1 2 5 2
2 3 3 4


Output

10


Input

2 3
5 6
5 5


Output

14

Note

In the second sample above, the Old Peykan stays in c1 for 3 hours.
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.File;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Enumeration;
import java.util.Iterator;
import java.util.Properties;

/**
 * Works good for CF
 * @author cykeltillsalu
 */
public class Prac {

	//some local config
	static boolean test = false;
	static String testDataFile = "testdata.txt";
	static String feedFile = "feed.txt";
	CompetitionType type = CompetitionType.CF;
	private static String ENDL = "\n";

	// solution
	private void solve() throws Throwable {
		
		
		int n = iread(), k = iread();
		int[] cost = new int[n], reload = new int[n];
		
		for (int i = 0; i < n; i++) {
			cost[i] = iread();
		}
		
		for (int i = 0; i < n; i++) {
			reload[i] = iread();
		}
		
		int fuel = 0, time = 0, max = 0;
		for (int i = 0; i < n; i++) {
			fuel += reload[i];
			max = Math.max(reload[i], max);
			while(fuel < cost[i]){
				fuel += max;
				time += k;
			}
			time += cost[i];
			fuel -= cost[i];
		}
		System.out.println(time);
		out.flush();
	}
	
	private boolean check(long hi, int i, long n) {
		String string = Long.valueOf(hi).toString();
		int sum = 0;
		for (int j = 0; j < string.length(); j++) {
			sum += string.charAt(j) - '0';
		}
		if(sum == i && hi*hi + i*hi - n == 0){
			return true;
		}
				
		return false;
	}

	public int iread() throws Exception {
		return Integer.parseInt(wread());
	}

	public double dread() throws Exception {
		return Double.parseDouble(wread());
	}

	public long lread() throws Exception {
		return Long.parseLong(wread());
	}

	public String wread() throws IOException {
		StringBuilder b = new StringBuilder();
		int c;
		c = in.read();
		while (c >= 0 && c <= ' ')
			c = in.read();
		if (c < 0)
			return "";
		while (c > ' ') {
			b.append((char) c);
			c = in.read();
		}
		return b.toString();
	}

	public static void main(String[] args) throws Throwable {
		
		if(test){ //run all cases from testfile:
			BufferedReader testdataReader = new BufferedReader(new FileReader(testDataFile));
			String readLine = testdataReader.readLine();
			int casenr = 0;
			out: while (true) {
				BufferedWriter w = new BufferedWriter(new FileWriter(feedFile));
				if(!readLine.equalsIgnoreCase("input")){
					break;
				}
				while (true) {
					readLine = testdataReader.readLine();
					if(readLine.equalsIgnoreCase("output")){
						break;
					}
					w.write(readLine + "\n");
				}
				w.close();
				System.out.println("Answer on case "+(++casenr)+": ");
				
				new Prac().solve();
				System.out.println("Expected answer: ");
				
				
				while (true) {
					readLine = testdataReader.readLine();
					
					if(readLine == null){
						break out;
					}
					if(readLine.equalsIgnoreCase("input")){
						break;
					}
					System.out.println(readLine);
				}
				System.out.println("----------------");
			}
			testdataReader.close();
		} else { // run on server
			new Prac().solve();
		}
		out.close();
	}

	public Prac() throws Throwable {
		if (test) {
			in = new BufferedReader(new FileReader(new File(feedFile)));
		}
	}

	InputStreamReader inp = new InputStreamReader(System.in);
	BufferedReader in = new BufferedReader(inp);
	static BufferedWriter out = new BufferedWriter(new OutputStreamWriter(System.out));
	
	enum CompetitionType {CF, OTHER};
}