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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define FAST std::ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define DECIMAL(n)  std::cout << std::fixed;std::cout << std::setprecision(n);
#define hell 1000000007
#define narak 998244353
#define PI 3.14159265358979323844
#define mp make_pair
#define eb emplace_back
#define pb push_back
#define fi first 
#define se second
#define all(v) v.begin(), v.end()
#define endl "\n"
#define sqr(a) (a)*(a)
#define __lcm(m,n) m*(n/__gcd(m,n))
#define inputarr(a,n) for(int xxx=0;xxx<n;++xxx) cin>>(a)[xxx]
#define sz(a) (int)a.size()
#define sl(a) (int)a.length()
#define display(x) for(auto &a:x) cout<<a<<" ";cout<<endl
#define debug cerr<<"bhau"<<endl
#define between(n,a,b) (a<=n&&n<=b)
#define elasped_time 1.0 * clock() / CLOCKS_PER_SEC 

#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1>
void __f(const char* name, Arg1&& arg1){
    std::cerr << name << " : " << arg1 << endl;
}
template <typename Arg1, typename... Args>
void __f(const char* names, Arg1&& arg1, Args&&... args){
    const char* comma = strchr(names + 1, ',');std::cerr.write(names, comma - names) << " : " << arg1<<" | ";__f(comma+1, args...);
}


template<typename T, typename U> static inline void amin(T &x, U y) { 
    if (y < x) 
        x = y; 
}

template<typename T, typename U> static inline void amax(T &x, U y) { 
    if (x < y) 
        x = y; 
}

template<typename T,typename U> std::ostream& operator<<(std::ostream& out, std::pair<T,U> a) {
    out<<a.fi<<" "<<a.se;
    return out;
}

template<typename T,typename U> std::istream& operator>>(std::istream& in, std::pair<T,U> &a) {
    in>>a.fi>>a.se;
    return in;
}

inline long long toint(const std::string &s) {std::stringstream ss; ss << s; long long x; ss >> x; return x;}
inline std::string tostring(long long number) {std::stringstream ss; ss << number; return ss.str();}
inline std::string tobin(long long x) {return std::bitset<63>(x).to_string();}

std::mt19937_64 rng(std::chrono::steady_clock::now().time_since_epoch().count());

#define ll long long
#define pii std::pair<int, int>
#define vi vector<int>  
#define vvi vector<vi > 
#define vii vector<pii >
#define point complex<ll>
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update> 

/*----------------------Graph Moves----------------*/
//const int fx[]={+1,-1,+0,+0};
//const int fy[]={+0,+0,+1,-1};
//const int fx[]={+0,+0,+1,-1,-1,+1,-1,+1};   // Kings Move
//const int fy[]={-1,+1,+0,+0,+1,+1,-1,-1};  // Kings Move
//const int fx[]={-2, -2, -1, -1,  1,  1,  2,  2};  // Knights Move
//const int fy[]={-1,  1, -2,  2, -2,  2, -1,  1}; // Knights Move
/*------------------------------------------------*/

//primes for hashing 937,991,1013,1409,1741

using namespace std;
using namespace __gnu_pbds;
#define int long long
void meowmeow321()
{
    int n,a,b;
    cin>>n>>a>>b;
    int x[n];
    inputarr(x,n);
    vector<int> diff;
    for (int i = 1; i < n; ++i) {
    	diff.pb((x[i]-x[i-1])*a);
    }
    for (int i = 0; i < n-1; ++i) {
    	amin(diff[i],b);
    }
    cout<<accumulate(all(diff),0ll);
}
signed main()
{
    FAST;
    int testcases=1;
    //cin>>testcases;
    for(int i=0;i<testcases;++i)
    {
        meowmeow321();
    }
    cerr<<endl<<"Time Elasped : "<<elasped_time<<endl;
    return 0;
}