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.

Input

Input is given from Standard Input in the following format:


N
x_1 x_2 \ldots x_N


Output

Print the answer.

Examples

Input

3
1 2 3


Output

5


Input

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


Output

750927044
import java.util.*;
import java.io.*;

class Main{
    static long MOD=1_000_000_007l;
    static long[] comb;
    static long[] fact;
    static long[] inv;
    public static void main(String[] args){
        FastScanner fsc=new FastScanner();
        int n=fsc.nextInt();
        long[] x=new long[n+1];
        long[] a=new long[n+1];
        for(int i=1;i<=n;i++){
            x[i]=fsc.nextLong();
            a[i]=x[i]+a[i-1];
        }
        fsc.close();
        long ans=0;
        // comb=new long[n];
        // for(int i=0;i<n;i++){
        //     if(i==0){
        //         comb[i]=1;
        //     } else{
        //         comb[i]=(((comb[i-1]*(n-i))%MOD)*modinv(i))%MOD;
        //     }
        // }
        fact=new long[n];
        for(int i=0;i<n;i++){
            if(i==0){
                fact[i]=1;
            } else{
                fact[i]=(fact[i-1]*i)%MOD;
            }
        }
        inv=new long[n+1];
        for(int i=1;i<=n;i++){
            inv[i]=modinv(i);
        }
        for(int i=1;i<n;i++){
            ans+=((x[n]-x[i])*inv[i])%MOD;
            ans%=MOD;
        }
        ans*=fact[n-1];
        ans%=MOD;
        System.out.println(ans);
        // long[] wj=new long[n-1];
        // for(int j=1;j<=n-2;j++){
        //     wj[j]=((a[n-1]-a[j])-a[n-j-1])%MOD;
        //     if(wj[j]<0){
        //         wj[j]+=MOD;
        //     }
        // }
        // long ans=0;
        // for(int j=1;j<=n-2;j++){
        //     ans+=(((wj[j]*inv[j])%MOD)*inv[j+1])%MOD;
        //     ans%=MOD;
        // }
        // ans*=fact[n-1];
        // ans%=MOD;
        // // for(int i=1;i<=n-1;i++){
        // //     for(int j=i+1;j<=n-1;j++){
        // //         ans+=(((fact[n-1]*(x[j]-x[i]))%MOD)*((inv[j-i+1]*inv[j-i])%MOD))%MOD;
        // //         ans%=MOD;
        // //     }
        // // }
        // for(int i=1;i<=n-1;i++){
        //     ans+=(((((fact[n-i-1]*comb[i-1])%MOD)*(x[n]-x[i]))%MOD)*fact[i-1])%MOD;
        //     ans%=MOD;
        // }
        // System.out.println(ans);
    }
    public static long modinv(long a) {
        long b = MOD;
        long u = 1, v = 0;
        while (b >= 1) {
            long t = a / b;
            a -= t * b;
            long tmp1 = a;
            a = b;
            b = tmp1;
            u -= t * v;
            long tmp2 = u;
            u = v;
            v = tmp2;
        }
        u %= MOD;
        return u >= 0 ? u : u + MOD;
    }

    public static long comb(long n, long r) {
        if (n < r){
            return 0;
        }
        if(r>0 && comb[(int)r-1]>0){
            return comb[(int)r]=((comb[(int)r-1]*(n-r))%MOD)*modinv(r);
        }
        r = Math.min(r, n - r);
        long res = 1;
        for (int d = 1; d <= r; d++) {
            res *= n;
            res %= MOD;
            n--;
            res *= modinv(d);
            res %= MOD;
        }
        return res;
    }
    static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte(){
            if(ptr<buflen) return true;
            else{
                ptr = 0;
                try{
                    buflen = in.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() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        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 || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
        public void close(){
            try{in.close();}
            catch(IOException e){e.printStackTrace();}
        }
    }
}
