Problem:
Score : 500 points

Problem Statement

There are N towns on a line running east-west.
The towns are numbered 1 through N, in order from west to east.
Each point on the line has a one-dimensional coordinate, and a point that is farther east has a greater coordinate value.
The coordinate of town i is X_i.

You are now at town 1, and you want to visit all the other towns.
You have two ways to travel:

Walk on the line.
Your fatigue level increases by A each time you travel a distance of 1, regardless of direction.

Teleport to any location of your choice.
Your fatigue level increases by B, regardless of the distance covered.

Find the minimum possible total increase of your fatigue level when you visit all the towns in these two ways.

Constraints

All input values are integers.

2≤N≤10^5

1≤X_i≤10^9

For all i(1≤i≤N-1), X_i<X_{i+1}.

1≤A≤10^9

1≤B≤10^9

Input

The input is given from Standard Input in the following format:

N A B
X_1 X_2 ... X_N

Output

Print the minimum possible total increase of your fatigue level when you visit all the towns.

Sample Input 1

4 2 5
1 2 5 7

Sample Output 1

11

From town 1, walk a distance of 1 to town 2, then teleport to town 3, then walk a distance of 2 to town 4.
The total increase of your fatigue level in this case is 2×1+5+2×2=11, which is the minimum possible value.

Sample Input 2

7 1 100
40 43 45 105 108 115 124

Sample Output 2

84

From town 1, walk all the way to town 7.
The total increase of your fatigue level in this case is 84, which is the minimum possible value.

Sample Input 3

7 1 2
24 35 40 68 72 99 103

Sample Output 3

12

Visit all the towns in any order by teleporting six times.
The total increase of your fatigue level in this case is 12, which is the minimum possible value.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.Closeable;
import java.io.FileInputStream;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.BitSet;
import java.util.HashMap;
import java.util.List;
import java.util.TreeMap;

public class Main implements Runnable{
	static ContestScanner in;static Writer out;
	public static void main(String[] args) {
		new Thread(null, new Main(), "", 16 * 1024 * 1024).start();
	}
	public void run() {
		try {
//			in = new ContestScanner("in.txt");
//			out = new Writer("out.txt");
			in = new ContestScanner();
			out = new Writer();
			Main solve = new Main();
			solve.solve();
			in.close();
			out.flush();
			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	static void dump(int[]a){StringBuilder s=new StringBuilder();for(int i=0;i<a.length;i++)
	s.append(a[i]).append(" ");out.println(s.toString().trim());}
	static void dump(int[]a,int n){for(int i=0;i<a.length;i++)out.printf("%"+n+"d ",a[i]);out.println();}
	static void dump(long[]a){StringBuilder s=new StringBuilder();for(int i=0;i<a.length;i++)
	s.append(a[i]).append(" ");out.println(s.toString().trim());}
	static void dump(char[]a){for(int i=0;i<a.length;i++)out.print(a[i]);out.println();}
	static long pow(long a,int n){long r=1;while(n>0){if((n&1)==1)r*=a;a*=a;n>>=1;}return r;}
	static String itob(int a,int l){return String.format("%"+l+"s",Integer.toBinaryString(a)).replace(' ','0');}
	static void sort(int[]a){m_sort(a,0,a.length,new int[a.length]);}
	static void sort(int[]a,int l){m_sort(a,0,l,new int[l]);}
	static void sort(int[]a,int l,int[]buf){m_sort(a,0,l,buf);}
	static void sort(int[]a,int s,int l,int[]buf){m_sort(a,s,l,buf);}
	static void m_sort(int[]a,int s,int sz,int[]b)
	{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
	m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
	while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
	while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];
	} /* qsort(3.5s)<<msort(9.5s)<<<shuffle+qsort(17s)<Arrays.sort(Integer)(20s) */
	static void sort(long[]a){m_sort(a,0,a.length,new long[a.length]);}
	static void sort(long[]a,int l){m_sort(a,0,l,new long[l]);}
	static void sort(long[]a,int l,long[]buf){m_sort(a,0,l,buf);}
	static void sort(long[]a,int s,int l,long[]buf){m_sort(a,s,l,buf);}
	static void m_sort(long[]a,int s,int sz,long[]b)
	{if(sz<7){for(int i=s;i<s+sz;i++)for(int j=i;j>s&&a[j-1]>a[j];j--)swap(a, j, j-1);return;}
	m_sort(a,s,sz/2,b);m_sort(a,s+sz/2,sz-sz/2,b);int idx=s;int l=s,r=s+sz/2;final int le=s+sz/2,re=s+sz;
	while(l<le&&r<re){if(a[l]>a[r])b[idx++]=a[r++];else b[idx++]=a[l++];}
	while(r<re)b[idx++]=a[r++];while(l<le)b[idx++]=a[l++];for(int i=s;i<s+sz;i++)a[i]=b[i];}
	static void swap(long[] a,int i,int j){final long t=a[i];a[i]=a[j];a[j]=t;}
	static void swap(int[] a,int i,int j){final int t=a[i];a[i]=a[j];a[j]=t;}
	static int binarySearchSmallerMax(int[]a,int v)// get maximum index which a[idx]<=v
	{int l=-1,r=a.length-1,s=0;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return s;}
	static int binarySearchSmallerMax(int[]a,int v,int l,int r)
	{int s=-1;while(l<=r){int m=(l+r)/2;if(a[m]>v)r=m-1;else{l=m+1;s=m;}}return s;}
	@SuppressWarnings("unchecked")
	static List<Integer>[]createGraph(int n)
    {List<Integer>[]g=new List[n];for(int i=0;i<n;i++)g[i]=new ArrayList<>();return g;}
	void solve() throws IOException{
		int n = in.nextInt();
		long a = in.nextInt();
		long b = in.nextLong();
		long pre = in.nextLong();
		long ans = 0;
		for(int i=1; i<n; i++){
			long x = in.nextLong();
			ans += Math.min((x-pre)*a, b);
			pre = x;
		}
		System.out.println(ans);
	}
}

@SuppressWarnings("serial")
class MultiSet<T> extends HashMap<T, Integer>{
	@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
	public MultiSet<T> merge(MultiSet<T> set)
	{MultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
	for(Entry<T,Integer>e:s.entrySet())l.add(e.getKey(),e.getValue());return l;}
}
@SuppressWarnings("serial")
class OrderedMultiSet<T> extends TreeMap<T, Integer>{
	@Override public Integer get(Object key){return containsKey(key)?super.get(key):0;}
	public void add(T key,int v){put(key,get(key)+v);}
	public void add(T key){put(key,get(key)+1);}
	public void sub(T key){final int v=get(key);if(v==1)remove(key);else put(key,v-1);}
	public OrderedMultiSet<T> merge(OrderedMultiSet<T> set)
	{OrderedMultiSet<T>s,l;if(this.size()<set.size()){s=this;l=set;}else{s=set;l=this;}
	while(!s.isEmpty()){l.add(s.firstEntry().getKey(),s.pollFirstEntry().getValue());}return l;}
}
class Pair implements Comparable<Pair>{
	int a,b;final int hash;Pair(int a,int b){this.a=a;this.b=b;hash=(a<<16|a>>16)^b;}
	public boolean equals(Object obj){Pair o=(Pair)(obj);return a==o.a&&b==o.b;}
	public int hashCode(){return hash;}
	public int compareTo(Pair o){if(a!=o.a)return a<o.a?-1:1;else if(b!=o.b)return b<o.b?-1:1;return 0;}
}
class Timer{
	long time;public void set(){time=System.currentTimeMillis();}
	public long stop(){return time=System.currentTimeMillis()-time;}
	public void print(){System.out.println("Time: "+(System.currentTimeMillis()-time)+"ms");}
	@Override public String toString(){return"Time: "+time+"ms";}
}
class Writer extends PrintWriter{
	public Writer(String filename)throws IOException
	{super(new BufferedWriter(new FileWriter(filename)));}
	public Writer()throws IOException{super(System.out);}
}
class ContestScanner implements Closeable{
	private BufferedReader in;private int c=-2;
	public ContestScanner()throws IOException 
	{in=new BufferedReader(new InputStreamReader(System.in));}
	public ContestScanner(String filename)throws IOException
	{in=new BufferedReader(new InputStreamReader(new FileInputStream(filename)));}
	public String nextToken()throws IOException {
		StringBuilder sb=new StringBuilder();
		while((c=in.read())!=-1&&Character.isWhitespace(c));
		while(c!=-1&&!Character.isWhitespace(c)){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public String readLine()throws IOException{
		StringBuilder sb=new StringBuilder();if(c==-2)c=in.read();
		while(c!=-1&&c!='\n'&&c!='\r'){sb.append((char)c);c=in.read();}
		return sb.toString();
	}
	public long nextLong()throws IOException,NumberFormatException
	{return Long.parseLong(nextToken());}
	public int nextInt()throws NumberFormatException,IOException
	{return(int)nextLong();}
	public double nextDouble()throws NumberFormatException,IOException 
	{return Double.parseDouble(nextToken());}
	public void close() throws IOException {in.close();}
}