Problem:
Score : 600 points

Problem Statement

There are N slimes standing on a number line.
The i-th slime from the left is at position x_i.

It is guaruanteed that 1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}.

Niwango will perform N-1 operations. The i-th operation consists of the following procedures:

Choose an integer k between 1 and N-i (inclusive) with equal probability.

Move the k-th slime from the left, to the position of the neighboring slime to the right.

Fuse the two slimes at the same position into one slime.

Find the total distance traveled by the slimes multiplied by (N-1)! (we can show that this value is an integer), modulo (10^{9}+7). If a slime is born by a fuse and that slime moves, we count it as just one slime.

Constraints

2 \leq N \leq 10^{5}

1 \leq x_1 < x_2 < \ldots < x_N \leq 10^{9}

x_i is an integer.

Subtasks

400 points will be awarded for passing the test cases satisfying N \leq 2000.

Input

Input is given from Standard Input in the following format:

N
x_1 x_2 \ldots x_N

Output

Print the answer.

Sample Input 1

3
1 2 3

Sample Output 1

5

With probability \frac{1}{2}, the leftmost slime is chosen in the first operation, in which case the total distance traveled is 2.

With probability \frac{1}{2}, the middle slime is chosen in the first operation, in which case the total distance traveled is 3.

The answer is the expected total distance traveled, 2.5, multiplied by 2!, which is 5.

Sample Input 2

12
161735902 211047202 430302156 450968417 628894325 707723857 731963982 822804784 880895728 923078537 971407775 982631932

Sample Output 2

750927044

Find the expected value multiplied by (N-1)!, modulo (10^9+7).

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;

public class Main{
  static int repow(int b,int p){
    long a = b;
    long res=1;
    while(p>0){
      if(p%2==1){
        res*=a;
      }
      a*=a;
      p/=2;
    }
    return (int)res;
  }
  static int repow(int b,int p,int modder){
    long a = b%modder;
    long res=1;
    while(p>0){
      if(p%2==1){
        res=(res*a)%modder;
      }
      a=(a*a)%modder;
      p/=2;
    }
    return (int)res;
  }
  static long repow(long b,long p){
    long a = b;
    long res=1;
    while(p>0){
      if(p%2==1){
        res*=a;
      }
      a*=a;
      p/=2;
    }
    return res;
  }
  static long repow(long b,long p,long modder){
    long a = b%modder;
    long res=1;
    while(p>0){
      if(p%2==1){
        res=(res*a)%modder;
      }
      a=(a*a)%modder;
      p/=2;
    }
    return res;
  }
  static long gcd(long c,long d){
    while(true){
      long f=c%d;
      if(f==0){
        return d;
      }
      c=d;
      d=f;
    }
  }
  static long lcm(long c,long d){
    return c/gcd(c,d)*d;
  }
  static ArrayList<Integer> divList(int n){
    ArrayList<Integer> div=new ArrayList<Integer>();
    for(int i=1;i*i<=n;i++){
      if(n%i==0){
        div.add(i);
        if(i*i!=n){
          div.add((int)(n/i));
        }
      }
    }
    return div;
  }
  static ArrayList<Long> divList(long n){
    ArrayList<Long> div=new ArrayList<Long>();
    for(long i=1;i*i<=n;i++){
      if(n%i==0){
        div.add(i);
        if(i*i!=n){
          div.add((n/i));
        }
      }
    }
    return div;
  }
  static ArrayList<Long> pDivList(long n){
    ArrayList<Long> div=new ArrayList<Long>();
    for(long i=1;i*i<=n;i++){
      if(n%i==0){
        if(iP(i)){
          div.add(i);
        }
        if(iP(n/i)&&i*i!=n){
          div.add((n/i));
        }
      }
    }
    return div;
  }
  static HashSet<Integer> divSet(int n){
    HashSet<Integer> div=new HashSet<Integer>();
    for(int i=1;i*i<=n;i++){
      if(n%i==0){
        div.add(i);
        div.add((int)(n/i));
      }
    }
    return div;
  }
  static boolean iP(long n){
    if(n==2){
      return true;
    }
    if((n&1)==0||n==1){
      return false;
    }
//    if(n>3037007383L){
    if(n>Integer.MAX_VALUE){
      return tameshiwari(n);
    }
    long d=n-1;
    int s=0;
    while((d&1)==0){
      d/=2;
      s++;
    }
    int[] aa = {2,3,5,7,11,13,17};
    for(int i=0;i<7&&aa[i]<n;i++){
      int a = aa[i];
      long t = d;
      long y=repow(a,t,n);
      while(t!=n-1&&y!=1&&y!=n-1){
        y = (y*y)%n;
        t=t<<1;
      }
      if(y!=n-1&&(t&1)==0){
        return false;
      }
    }
    return true;
  }
  static boolean tameshiwari(long n){
    for(long i=2;i*i<=n;i++){
      if(n%i==0){
        return false;
      }
    }
    return true;
  }
  static class NCK{
    int max;
    int modder;
    long[] fac;
    long[] finv;
    long[] inv;
    NCK(){
      this(510000,1000000007);
    }
    NCK(int max,int modder){
      this.max=max;
      this.modder=modder;
      pre();
    }
    void pre(){
      fac = new long[max];
      finv = new long[max];
      inv = new long[max];
      fac[0]=fac[1]=1;
      finv[0]=finv[1]=1;
      inv[1]=1;
      for(int i=2;i<max;i++){
        fac[i]=fac[i-1]*i%modder;
        inv[i]=modder-inv[modder%i]*(modder/i)%modder;
        finv[i]=finv[i-1]*inv[i]%modder;
      }
    }
    long nCk(int n,int k){
      if(n<k){return 0;}
      if(n<0||k<0){return 0;}
      return fac[n]*(finv[k]*finv[n-k]%modder)%modder;
    }
  }
  static <T extends Comparable<T>> int BSA(List<T> l,T target){
    return BSA(l,target,0,l.size(),(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSA(List<T> l,T target,Comparator<T> c){
    return BSA(l,target,0,l.size(),c);
  }
  static <T extends Comparable<T>> int BSA(List<T> l,T target,int left,int right){
    return BSA(l,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSA(List<T> l,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=l.get(lt+(rt-lt)/2);
      if(c.compare(gaze,target)<0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>0){
        rt=lt+(rt-lt)/2-1;
      }else{
        return lt+(rt-lt)/2;
      }
    }
    return -1;
  }
  static <T extends Comparable<T>> int BSF(List<T> l,T target){
    return BSF(l,target,0,l.size(),(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSF(List<T> l,T target,Comparator<T> c){
    return BSF(l,target,0,l.size(),c);
  }
  static <T extends Comparable<T>> int BSF(List<T> l,T target,int left,int right){
    return BSF(l,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSF(List<T> l,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=l.get(lt+(rt-lt)/2);
      if(c.compare(gaze,target)<0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>=0){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static <T extends Comparable<T>> int BSL(List<T> l,T target){
    return BSL(l,target,0,l.size(),(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSL(List<T> l,T target,Comparator<T> c){
    return BSL(l,target,0,l.size(),c);
  }
  static <T extends Comparable<T>> int BSL(List<T> l,T target,int left,int right){
    return BSL(l,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSL(List<T> l,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=l.get(lt+(rt-lt)/2);
      if(c.compare(gaze,target)<=0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>0){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static <T extends Comparable<T>> int BSA(T[] a,T target){
    return BSA(a,target,0,a.length,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSA(T[] a,T target,Comparator<T> c){
    return BSA(a,target,0,a.length,c);
  }
  static <T extends Comparable<T>> int BSA(T[] a,T target,int left,int right){
    return BSA(a,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSA(T[] a,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=a[lt+(rt-lt)/2];
      if(c.compare(gaze,target)<0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>0){
        rt=lt+(rt-lt)/2-1;
      }else{
        return lt+(rt-lt)/2;
      }
    }
    return -1;
  }
  static <T extends Comparable<T>> int BSF(T[] a,T target){
    return BSF(a,target,0,a.length,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSF(T[] a,T target,Comparator<T> c){
    return BSF(a,target,0,a.length,c);
  }
  static <T extends Comparable<T>> int BSF(T[] a,T target,int left,int right){
    return BSF(a,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSF(T[] a,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=a[lt+(rt-lt)/2];
      if(c.compare(gaze,target)<0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>=0){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static <T extends Comparable<T>> int BSL(T[] a,T target){
    return BSL(a,target,0,a.length,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSL(T[] a,T target,Comparator<T> c){
    return BSL(a,target,0,a.length,c);
  }
  static <T extends Comparable<T>> int BSL(T[] a,T target,int left,int right){
    return BSL(a,target,left,right,(s1,s2)->s1.compareTo(s2));
  }
  static <T> int BSL(T[] a,T target,int left,int right,Comparator<T> c){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      T gaze=a[lt+(rt-lt)/2];
      if(c.compare(gaze,target)<=0){
        lt=lt+(rt-lt)/2+1;
      }else if(c.compare(gaze,target)>0){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int BSA(int[] a,int target){
    return BSA(a,target,0,a.length,true);
  }
  static int BSA(int[] a,int target, boolean syojun){
    return BSA(a,target,0,a.length,syojun);
  }
  static int BSA(int[] a,int target,int left,int right){
    return BSA(a,target,left,right,true);
  }
  static int BSA(int[] a,int target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      int gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<target)||(!syojun&&gaze>target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze>target)||(!syojun&&gaze<target)){
        rt=lt+(rt-lt)/2-1;
      }else{
        return lt+(rt-lt)/2;
      }
    }
    return -1;
  }
  static int BSF(int[] a,int target){
    return BSF(a,target,0,a.length,true);
  }
  static int BSF(int[] a,int target,boolean syojun){
    return BSF(a,target,0,a.length,syojun);
  }
  static int BSF(int[] a,int target,int left,int right){
    return BSF(a,target,left,right,true);
  }
  static int BSF(int[] a,int target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      int gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<target)||(!syojun&&gaze>target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze<=target)||(!syojun&&gaze>=target)){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int BSL(int[] a,int target){
    return BSL(a,target,0,a.length,true);
  }
  static int BSL(int[] a,int target,boolean syojun){
    return BSL(a,target,0,a.length,syojun);
  }
  static int BSL(int[] a,int target,int left,int right){
    return BSL(a,target,left,right,true);
  }
  static int BSL(int[] a,int target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      int gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<=target)||(!syojun&&gaze>=target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze>target)||(!syojun&&gaze<target)){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int BSA(long[] a,long target){
    return BSA(a,target,0,a.length,true);
  }
  static int BSA(long[] a,long target, boolean syojun){
    return BSA(a,target,0,a.length,syojun);
  }
  static int BSA(long[] a,long target,int left,int right){
    return BSA(a,target,left,right,true);
  }
  static int BSA(long[] a,long target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      long gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<target)||(!syojun&&gaze>target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze>target)||(!syojun&&gaze<target)){
        rt=lt+(rt-lt)/2-1;
      }else{
        return lt+(rt-lt)/2;
      }
    }
    return -1;
  }
  static int BSF(long[] a,long target){
    return BSF(a,target,0,a.length,true);
  }
  static int BSF(long[] a,long target,boolean syojun){
    return BSF(a,target,0,a.length,syojun);
  }
  static int BSF(long[] a,long target,int left,int right){
    return BSF(a,target,left,right,true);
  }
  static int BSF(long[] a,long target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      long gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<target)||(!syojun&&gaze>target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze<=target)||(!syojun&&gaze>=target)){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int BSL(long[] a,long target){
    return BSL(a,target,0,a.length,true);
  }
  static int BSL(long[] a,long target,boolean syojun){
    return BSL(a,target,0,a.length,syojun);
  }
  static int BSL(long[] a,long target,int left,int right){
    return BSL(a,target,left,right,true);
  }
  static int BSL(long[] a,long target,int left,int right,boolean syojun){
    int lt = left;
    int rt = right-1;
    while(lt<=rt){
      long gaze=a[lt+(rt-lt)/2];
      if((syojun&&gaze<=target)||(!syojun&&gaze>=target)){
        lt=lt+(rt-lt)/2+1;
      }else if((syojun&&gaze>target)||(!syojun&&gaze<target)){
        rt=lt+(rt-lt)/2-1;
      }
    }
    return lt;
  }
  static int kmp(String t,String p){
    int[] f=new int[p.length()+1];
    int i=0;
    int j=1;
    f[1]=0;
    while(j<p.length()){
      if(i==0||p.charAt(i-1)==p.charAt(j-1)){
        i++;
        j++;
        f[j]=i;
      }else{
        i=f[i];
      }
    }
    i=1;
    j=1;
    while(i<=p.length()&&j<=t.length()){
      if(i==0||p.charAt(i-1)==t.charAt(j-1)){
        i++;
        j++;
      }else{
        i=f[i];
      }
    }
    return i==(p.length()+1)?j-i:-1;
  }
  static String StSort(String s){
    StringBuilder sb = new StringBuilder(s);
    int lg = sb.length();
    int l;
    int r;
    int gaze;
    for(int i=1;i<lg;i++){
      l=0;
      r=i-1;
      while(l<=r){
        gaze=(l+r)/2;
        if(sb.charAt(gaze)<=sb.charAt(i)){
          l=gaze+1;
        }else if(sb.charAt(gaze)>sb.charAt(i)){
          r=gaze-1;
        }
      }
      sb.insert(l,sb.charAt(i));
      sb.deleteCharAt(i+1);
    }
    return sb.toString();
  }
  static class Xy{
    int x;
    int y;
    Xy(int x,int y){
      this.x=x;
      this.y=y;
    }
    public int manht(Xy o){
      return Math.abs(x-o.x)+Math.abs(y-o.y);
    }
    public String toString(){
      return "["+x+","+y+"]";
    }
    public double henkaku(){
      return Math.atan2(y,x);
    }
    public static int hencom(Xy s1,Xy s2){
      return (int)Math.signum(s1.henkaku()-s2.henkaku());
    }
    public boolean equals(Object o){
      return x==((Xy)o).x&&y==((Xy)o).y;
    }
  }
  static class UnFd{
    int n;
    int[] a;
    int forest;
    UnFd(int n){
      forest=this.n=n;
      a = new int[n];
      for(int i=0;i<n;i++){
        a[i] = i;
      }
    }
    boolean isRoot(int i){
      return a[i]==i;
    }
    int rootOf(int i){
      if(isRoot(i)){
        return i;
      }
      return a[i] = rootOf(a[i]);
    }
    boolean ud(int i,int j){
      return rootOf(i)==rootOf(j);
    }
    boolean marge(int i,int j){
      if(ud(i,j)){
        return false;
      }
      i=rootOf(i);
      j=rootOf(j);
      a[Integer.max(i,j)]=Integer.min(i,j);
      forest-=1;
      return true;
    }
    int[] roots(){
      int[] rs = new int[forest];
      int p=0;
      for(int i=0;i<n;i++){
        if(isRoot(i)){
          rs[p]=i;
          p++;
        }
      }
      return rs;
    }
  }
  static class Scnr{
    private final InputStream ins;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    Scnr(){
      this(System.in);
    }
    Scnr(InputStream in){
      ins = in;
    }
    private boolean hasNextByte(){
      if(ptr<buflen){
        return true;
      }else{
        ptr = 0;
        try{
          buflen = ins.read(buffer);
        }catch(IOException e){
          e.printStackTrace();
        }
        if(buflen<=0){
          return false;
        }
      }
      return true;
    }
    private int readByte(){
      if(hasNextByte()){
        return buffer[ptr++];
      }else{
        return -1;
      }
    }
    private static boolean isPrintableChar(int c){
      return 33<=c&&c<=126;
    }
    public boolean hasNext(){
      while(hasNextByte()&&!isPrintableChar(buffer[ptr])){
        ptr++;
      }
      return hasNextByte();
    }
    public String next(){
      return nextBuilder().toString();
    }
    public StringBuilder nextBuilder(){
      if(!hasNext()){
        throw new NoSuchElementException();
      }
      StringBuilder sb = new StringBuilder();
      int b = readByte();
      while(isPrintableChar(b)){
        sb.appendCodePoint(b);
        b = readByte();
      }
      return sb;
    }
    public double nextDouble(){
      return Double.parseDouble(next());
    }
    public long nextLong(){
      if(!hasNext()){
        throw new NoSuchElementException();
      }
      long n = 0;
      boolean minus = false;
      int b = readByte();
      if(b=='-'){
        minus=true;
        b=readByte();
      }
      if(b<'0'||'9'<b){
        throw new NumberFormatException();
      }
      while(true){
        if('0'<=b&&b<='9'){
          n*=10;
          n+=b-'0';
        }else if(b==-1||!isPrintableChar(b)){
          return minus?-n:n;
        }else{
          throw new NumberFormatException();
        }
        b=readByte();
      }
    }
    public int nextInt(){
      long nl=nextLong();
      if(nl<Integer.MIN_VALUE||Integer.MAX_VALUE<nl){
        throw new NumberFormatException();
      }
      return (int) nl;
    }
    public int[] nextAInt(int n){
      int[] a = new int[n];
      nextAInt(a,n);
      return a;
    }
    public void nextAInt(int[] a,int n){
      nextAInt(a,0,n);
    }
    public void nextAInt(int[] a,int off,int len){
      for(int i=off;i<off+len;i++){
        a[i] = nextInt();
      }
    }
    public long[] nextALong(int n){
      long[] a = new long[n];
      nextALong(a,n);
      return a;
    }
    public void nextALong(long[] a,int n){
      nextALong(a,0,n);
    }
    public void nextALong(long[] a,int off,int len){
      for(int i=off;i<off+len;i++){
        a[i] = nextLong();
      }
    }
    public double[] nextADouble(int n){
      double[] a = new double[n];
      nextADouble(a,n);
      return a;
    }
    public void nextADouble(double[] a,int n){
      nextADouble(a,0,n);
    }
    public void nextADouble(double[] a,int off,int len){
      for(int i=off;i<off+len;i++){
        a[i] = nextDouble();
      }
    }
    public List<Integer> nextLInt(int n){
      List<Integer> l = new ArrayList<>(n);
      for(int i=0;i<n;i++){
        l.add(sc.nextInt());
      }
      return l;
    }
    public List<Long> nextLLong(int n){
      List<Long> l = new ArrayList<>(n);
      for(int i=0;i<n;i++){
        l.add(sc.nextLong());
      }
      return l;
    }
    public List<Double> nextLDouble(int n){
      List<Double> l = new ArrayList<>(n);
      for(int i=0;i<n;i++){
        l.add(sc.nextDouble());
      }
      return l;
    }
  }
  
  static Scnr sc = new Scnr();
  static PrintWriter out = new PrintWriter(System.out);
  public static void main(String args[]){
    int mod=1000_000_007;
    int n=sc.nextInt();
    if(n<=2500){
      
    }else{
      return;
    }
    int[] x=sc.nextAInt(n);
    int[] sa=new int[n-1];
    for(int i=0;i<n-1;i++){
      sa[i]=x[i+1]-x[i];
    }
    long[] kou=new long[n-1];
    kou[0]=1;
    long sf=1;
    for(int i=2;i<n;i++){
      for(int j=0;j<i-1;j++){
        kou[j]=(kou[j]*i)%mod;
      }
      kou[i-1]=(kou[i-2]+sf)%mod;
      sf=(sf*i)%mod;
//      System.out.println(Arrays.toString(kou));
    }
    long ans=0;
    for(int i=0;i<n-1;i++){
      ans=ans+(sa[i]*kou[i])%mod;
      ans=ans%mod;
    }
    out.println(ans);
    out.flush();
  }
}