[Sakuzyo - Imprinting](https://www.youtube.com/watch?v=55Ca6av1kAY)

A.R.C. Markland-N is a tall building with n floors numbered from 1 to n. Between each two adjacent floors in the building, there is a staircase connecting them.

It's lunchtime for our sensei Colin "ConneR" Neumann Jr, and he's planning for a location to enjoy his meal.

ConneR's office is at floor s of the building. On each floor (including floor s, of course), there is a restaurant offering meals. However, due to renovations being in progress, k of the restaurants are currently closed, and as a result, ConneR can't enjoy his lunch there.

CooneR wants to reach a restaurant as quickly as possible to save time. What is the minimum number of staircases he needs to walk to reach a closest currently open restaurant.

Please answer him quickly, and you might earn his praise and even enjoy the lunch with him in the elegant Neumanns' way!

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases in the test. Then the descriptions of t test cases follow.

The first line of a test case contains three integers n, s and k (2 ≤ n ≤ 10^9, 1 ≤ s ≤ n, 1 ≤ k ≤ min(n-1, 1000)) — respectively the number of floors of A.R.C. Markland-N, the floor where ConneR is in, and the number of closed restaurants.

The second line of a test case contains k distinct integers a_1, a_2, …, a_k (1 ≤ a_i ≤ n) — the floor numbers of the currently closed restaurants.

It is guaranteed that the sum of k over all test cases does not exceed 1000.

Output

For each test case print a single integer — the minimum number of staircases required for ConneR to walk from the floor s to a floor with an open restaurant.

Example

Input


5
5 2 3
1 2 3
4 3 3
4 1 2
10 2 6
1 2 3 4 5 7
2 1 1
2
100 76 8
76 75 36 67 41 74 10 77


Output


2
0
4
0
2

Note

In the first example test case, the nearest floor with an open restaurant would be the floor 4.

In the second example test case, the floor with ConneR's office still has an open restaurant, so Sensei won't have to go anywhere.

In the third example test case, the closest open restaurant is on the 6-th floor.
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
	static  ArrayList<Integer>adj[];
	static PrintWriter out=new PrintWriter(System.out);
	 public static int mod = 1000000007;

	static int notmemo[][][][];
	static int k;
	static long a[];
	static long b[];
	static int m;
	static char c[];
	static int trace[];
	public static void main(String[] args) throws Exception {
	Scanner sc=new Scanner(System.in);
	int t=sc.nextInt();
	while(t-->0) {
		int n=sc.nextInt();
		int s=sc.nextInt();
		int k=sc.nextInt();
		HashSet<Integer> set= new HashSet<Integer>();
		for (int i = 0; i < k; i++) {
			set.add(sc.nextInt());
		}
		//System.out.println(Arrays.toString(a));
		int min=(int) 1e9;
		for (int i = s; i <s+1002&&i<n+1; i++) {
		if(!set.contains(i)) {
			min=i-s;
			break;
		}
		}
		
		for (int i = s; i>=s-1002&&i>0; i--) {
			if(!set.contains(i)) {
				min=Math.min(min, s-i);
				break;
			}
		}
		out.println(min);
	}
	out.flush();
	}
	static int dp(int i,int even,int odd,int prev ) {
		if(i==n) {
			return 0;
		}
		if(notmemo[i][even][odd][prev]!=-1) {
			return notmemo[i][even][odd][prev];
		}
		int ans=(int) 1e9;
		
		if(a[i]!=0) {
			
			ans=Math.min(ans,dp(i+1,even,odd,(int) a[i]));
		}
		
		else if(even>0&&odd>0) {
			int countev=0;
			int countodd=0;
			if(i+1<n) {
				if(a[i+1]==1) {
					countev++;
				}
				else if(a[i+1]==2) {
					countodd++;
				}				
			}
			if(i-1>=0) {
				if(prev==1) {
					countev++;
				}
				else if(prev==2) {
					countodd++;
				}
			}
			ans=Math.min(ans, dp(i+1, even-1, odd,2)+countev);
			ans=Math.min(ans, dp(i+1, even, odd-1,1)+countodd);
		}
		else if(even>0) {
			int countev=0;
			if(i+1<n) {
				if(a[i+1]==1) {
					countev++;
				}				
			}
			if(i-1>=0) {
				if(prev==1) {
					countev++;
				}
			}
			ans=Math.min(ans, dp(i+1, even-1, odd,2)+countev);
		}
		else  {
			int countodd=0;
			
			if(i+1<n) {
				
				 if(a[i+1]==2) {
					countodd++;
				}				
			}
			if(i-1>=0) {
				
				if(prev==2) {
					countodd++;
				}
			}
			ans=Math.min(ans, dp(i+1, even, odd-1,1)+countodd);
		
		}
		return notmemo[i][even][odd][prev]=ans;

	}

	static long nCr1(int n , int k)
	{
		if(n < k)
			return 0;
		if(k == 0 || k == n)
			return 1;
		if(comb[n][k] != -1)
			return comb[n][k];
		if(n - k < k)
			return comb[n][k] = nCr1(n, n - k);
		return comb[n][k] = ((nCr1(n - 1, k - 1)%mod) +( nCr1(n - 1, k)%mod))%mod;
	}
	static void dfs(int u) {
		vis[u]=true;
		for(int v:adj[u]) {
			if(!vis[v]) {
				count++;
				dfs(v);
			}
		}
	}
	
	static int teams=0;
static long mini[];
static char x[]= {'h','a','r','d'};
static long s[];
static ArrayList<Integer> l1=new ArrayList<>();
static long count=0;


static class UnionFind {                                              
	int[] p, rank, setSize;
	int numSets;
	int max[];
	public UnionFind(int N) 
	{
		max=new int[N];
		p = new int[numSets = N];
		rank = new int[N];
		setSize = new int[N];
		for (int i = 0; i < N; i++) {  p[i] = i; setSize[i] = 1;
		max[i]=i;
		}
	}

	public int findSet(int i) { return p[i] == i ? i : (p[i] = findSet(p[i])); }

	public boolean isSameSet(int i, int j) { return findSet(i) == findSet(j); }

	public void unionSet(int i, int j) 
	{ 
		if (isSameSet(i, j)) 
			return;
		numSets--; 
		int x = findSet(i), y = findSet(j);
		if(rank[x] > rank[y]) { p[y] = x; setSize[x] += setSize[y];
		max[x]=Math.max(max[x], max[y]);
		
		}
		else
		{	p[x] = y; setSize[y] += setSize[x];
			if(rank[x] == rank[y]) rank[y]++; 
			max[y]=Math.max(max[x],max[y]);
			
		} 
	}

	private int getmax(int j) {
	return max[findSet(j)];
	}

	public int numDisjointSets() { return numSets; }

	public int sizeOfSet(int i) { return setSize[findSet(i)]; }
}





private static int bs(int i) {
	int high=n-1;
	int low=i;
	int ans=-1;
	int count=1;
	while(high>=low) {
	int	mid=(high+low)>>1;
	if(a[mid]-a[i]<=5) {
		ans=mid;
		low=mid+1;
		count=mid-i+1;
	}
	else {
		high=mid-1;
		
	}
	}
	return count;
	
	
}



/**private static void trace(int i, int time) {
if(i==n) 
	return;


long ans=dp(i,time);
if(time+a[i].t<a[i].burn&&(ans==dp(i+1,time+a[i].t)+a[i].cost)) {
	
	trace(i+1, time+a[i].t);
    
	l1.add(a[i].idx);
    return;
}
    trace(i+1,time);

}**/



	static class incpair implements Comparable<incpair>
{
	int a; long b;
	int idx;
	incpair(int a, long dirg,int i) {this.a = a;	b = dirg; idx=i; }
	
	public int compareTo(incpair e){ return (int) (b - e.b);	}
}
	static class decpair implements Comparable<decpair>
{
	int a; long b;int idx;
	
	decpair(int a, long dirg,int i) {this.a = a;	b = dirg; idx=i;}
	
	public int compareTo(decpair e){ return (int) (e.b- b);	}
}

	
	
	
	
	
	


	static long allpowers[];
	static class Quad implements Comparable<Quad>{
		int u;
		int v;
		char state;
		int turns;
		public Quad(int i, int j, char c, int k) {
		u=i;
		v=j;
		state=c;
		turns=k;
		}
		public int compareTo(Quad e){ return (int) (turns - e.turns);	}
		
	}
	static long dirg[][];
	static Edge[] driver;
	
	static int n;
		static class Edge implements Comparable<Edge>
	{
		int node; long cost;
		
		Edge(int a, long dirg) { node = a;	cost = dirg; }
		
		public int compareTo(Edge e){ return (int) (cost - e.cost);	}
	}

	



	  static long manhatandistance(long x,long x2,long y,long y2) {
		  return  Math.abs(x-x2)+Math.abs(y-y2);
	  }
	  static long fib[];
	  static long fib(int n) {
		  if(n==1||n==0) {
			  return 1;
		  }
		  if(fib[n]!=-1) {
			  return fib[n];
		  }
		  else 
			  return  fib[n]=  ((fib(n-2)%mod+fib(n-1)%mod)%mod);
	  }
	  static class Pair implements Comparable<Pair>{
		  long val;
		  int idx;
		  Pair(int a, long b){
			  idx=a;
			  val=b;
		  }
		public int compareTo(Pair p) {
		
			return (int) (this.val-p.val);
		}
		  
		  
	
		
		
	}
	static long[][] comb;		
	
	
	
static  class Triple implements Comparable<Triple>{

int t;
int burn;
		int cost;
		int idx;
		public Triple(int a,int b,int l,int i) {
			t=a;
			burn=b;
			cost=l;
			idx=i;
		}
		@Override
		public int compareTo(Triple o) {
			return Long.compare( burn,o.burn);	
		}
		
	}
	
	static TreeSet<Long> primeFactors(long N)		// O(sqrt(N) / ln sqrt(N))
	{
		TreeSet<Long> factors = new TreeSet<Long>();		//take abs(N) in case of -ve integers
		int idx = 0, p = primes.get(idx);

		while(p * p <= N)
		{
			while(N % p == 0) { factors.add((long) p); N /= p; }
			if(primes.size()>idx+1)
			p = primes.get(++idx);
			else
				break;
		}

		if(N != 1)						// last prime factor may be > sqrt(N)
			factors.add(N);				// for integers whose largest prime factor has a power of 1
		return factors;
	}
	
	static boolean visited[];
	/**static int bfs(int s)
	{
		Queue<Integer> q = new LinkedList<Integer>();
		q.add(s);
		int count=0;
		int maxcost=0;
		int dist[]=new int[n];
		dist[s]=0;
		while(!q.isEmpty())
		{
			
			int u = q.remove();
			if(dist[u]==k) {
				break;
			}
			for(Pair v: adj[u])
			{	
				maxcost=Math.max(maxcost, v.cost);
			
			
			
			if(!visited[v.v])	{
				
				visited[v.v]=true;
				q.add(v.v);
				dist[v.v]=dist[u]+1;
				maxcost=Math.max(maxcost, v.cost);
			}
			}	
			
		}
		return maxcost;
	}**/
	public static boolean FindAllElements(int n, int k) {
	 int sum = k;  
     int[] A = new int[k];  
      Arrays.fill(A, 0, k, 1);  
        
      for (int i = k - 1; i >= 0; --i) {  
      
           while (sum + A[i] <= n) {  
      
              sum += A[i];  
              A[i] *= 2;  
          }  
      }  
      if(sum==n) {
      	return true;
      }
      else
    	return false; 
	}
	
	static long[][] memo;

	
	static boolean vis2[][];
	
	static class SegmentTree {		// 1-based DS, OOP
		
		int N; 			//the number of elements in the array as a power of 2 (i.e. after padding)
		int[] array, sTree, lazy;
		
		SegmentTree(int[] in)		
		{
			array = in; N = in.length - 1;
			sTree = new int[N<<1];		//no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new int[N<<1];
			build(1,1,N);
		}
		
		void build(int node, int b, int e)	// O(n)
		{
			if(b == e)					
				sTree[node] = array[b];
			else						
			{
				int mid = b + e >> 1;
				build(node<<1,b,mid);
				build(node<<1|1,mid+1,e);
				sTree[node] = sTree[node<<1]+sTree[node<<1|1];
			}
		}
		
		
		void update_point(int index, int val)			// O(log n)
		{
			index += N - 1;				
			sTree[index] += val;			
			while(index>1)				
			{
				index >>= 1;
				sTree[index] = sTree[index<<1] + sTree[index<<1|1];		
			}
		}
		
		
		void update_range(int i, int j, int val)		// O(log n) 
		{
			update_range(1,1,N,i,j,val);
		}
		
		void update_range(int node, int b, int e, int i, int j, int val)
		{
			if(i > e || j < b)		
				return;
			if(b >= i && e <= j)		
			{
				sTree[node] += (e-b+1)*val;			
				lazy[node] += val;				
			}							
			else		
			{
				int mid = b + e >> 1;
				propagate(node, b, mid, e);
				update_range(node<<1,b,mid,i,j,val);
				update_range(node<<1|1,mid+1,e,i,j,val);
				sTree[node] = sTree[node<<1] + sTree[node<<1|1];		
			}
			
		}
		void propagate(int node, int b, int mid, int e)		
		{
			lazy[node<<1] += lazy[node];
			lazy[node<<1|1] += lazy[node];
			sTree[node<<1] += (mid-b+1)*lazy[node];		
			sTree[node<<1|1] += (e-mid)*lazy[node];		
			lazy[node] = 0;
		}
		
		int query(int i, int j)
		{
			return query(1,1,N,i,j);
		}
		
		int query(int node, int b, int e, int i, int j)	// O(log n)
		{
			if(i>e || j <b)
				return 0;		
			if(b>= i && e <= j)
				return sTree[node];
			int mid = b + e >> 1;
			propagate(node, b, mid, e);
			int q1 = query(node<<1,b,mid,i,j);
			int q2 = query(node<<1|1,mid+1,e,i,j);
			return q1 + q2;	
					
		}
	
	}
	static boolean f2=false;
	static long[][] matMul(long[][] a2, long[][] b, int p, int q, int r)	//C(p x r) = A(p x q) x (q x r) -- O(p x q x r)
	{
		long[][] C = new long[p][r];
		for(int i = 0; i < p; ++i) {
			for(int j = 0; j < r; ++j) {
				for(int k = 0; k < q; ++k) {
					C[i][j] = (C[i][j]+(a2[i][k]%mod * b[k][j]%mod))%mod;
		 C[i][j]%=mod;
				}
		
			}
		}
		return C;
	}
		
	
	
		
		
		
		

		
	
	static ArrayList<Pair> a1[];
	static int memo1[];
	
	static boolean vis[];
	static TreeSet<Integer> set=new TreeSet<Integer>();
	
	static long modPow(long ways, long count, long mod)	// O(log e)
	{
		ways %= mod;
		long res = 1;
		while(count > 0)
		{
			if((count & 1) == 1)
				res = (res * ways) % mod;
			ways = (ways * ways) % mod;
			count >>= 1;
		}
		return res%mod;
	}
	
	
	

	static long gcd(long ans,long b) {
		if(b==0) {
			return ans;
		}
		return gcd(b,ans%b);
	}
	static int[] isComposite;
	static int[] valid;
	
	static ArrayList<Integer> primes;
	static ArrayList<Integer> l;
	static void sieve(int N)	// O(N log log N) 
	{
		isComposite = new int[N+1];					
		isComposite[0] = isComposite[1] = 1;			// 0 indicates a prime number
		primes = new ArrayList<Integer>();
		l=new ArrayList<>();
		valid=new int[N+1];
		for (int i = 2; i <= N; ++i) 					//can loop till i*i <= N if primes array is not needed O(N log log sqrt(N)) 
			if (isComposite[i] == 0) 					//can loop in 2 and odd integers for slightly better performance
			{
				primes.add(i);
				l.add(i);
				valid[i]=1;
				
				for (int j = i*2; j <=N; j +=i) {	// j = i * 2 will not affect performance too much, may alter in modified sieve
						isComposite[j] = 1;
						
						
						
				      
					}
			}
		
		for(int i=0 ; i<primes.size() ; i++) {
			for(int j:primes) {
				if(primes.get(i)*j>N) {
					break;
				}
				valid[primes.get(i)*j]=1;
			}
		}
	}
	
	public static long[] schuffle(long[] a2) {
		for (int i = 0; i < a2.length; i++) {
			int x=(int)(Math.random()*a2.length);
		long temp=a2[x];
		a2[x]=a2[i];
		a2[i]=temp;
		}
		return a2;
	}
		static int V;
	static long INF=(long) 1E16;
		
		static class Edge2 
		{
			int node;
		long cost;
			long next;
			Edge2(int a, int c,Long long1) { node = a;	cost = long1; next=c;}
			
		}
static class Scanner {
		StringTokenizer st;
		BufferedReader br;
 
		public Scanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public Scanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
 
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public Long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}	
}