Problem: Nastya just made a huge mistake and dropped a whole package of rice on the floor. Mom will come soon. If she sees this, then Nastya will be punished.

In total, Nastya dropped n grains. Nastya read that each grain weighs some integer number of grams from a - b to a + b, inclusive (numbers a and b are known), and the whole package of n grains weighs from c - d to c + d grams, inclusive (numbers c and d are known). The weight of the package is the sum of the weights of all n grains in it.

Help Nastya understand if this information can be correct. In other words, check whether each grain can have such a mass that the i-th grain weighs some integer number x_i (a - b ≤ x_i ≤ a + b), and in total they weigh from c - d to c + d, inclusive (c - d ≤ ∑_{i=1}^{n}{x_i} ≤ c + d).

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. 

The next t lines contain descriptions of the test cases, each line contains 5 integers: n (1 ≤ n ≤ 1000) — the number of grains that Nastya counted and a, b, c, d (0 ≤ b < a ≤ 1000, 0 ≤ d < c ≤ 1000) — numbers that determine the possible weight of one grain of rice (from a - b to a + b) and the possible total weight of the package (from c - d to c + d).

Output

For each test case given in the input print "Yes", if the information about the weights is not inconsistent, and print "No" if n grains with masses from a - b to a + b cannot make a package with a total mass from c - d to c + d.

Example

Input


5
7 20 3 101 18
11 11 10 234 2
8 9 7 250 122
19 41 21 321 10
3 10 8 6 1


Output


Yes
No
Yes
No
Yes

Note

In the first test case of the example, we can assume that each grain weighs 17 grams, and a pack 119 grams, then really Nastya could collect the whole pack.

In the third test case of the example, we can assume that each grain weighs 16 grams, and a pack 128 grams, then really Nastya could collect the whole pack.

In the fifth test case of the example, we can be assumed that 3 grains of rice weigh 2, 2, and 3 grams, and a pack is 7 grams, then really Nastya could collect the whole pack.

In the second and fourth test cases of the example, we can prove that it is impossible to determine the correct weight of all grains of rice and the weight of the pack so that the weight of the pack is equal to the total weight of all collected grains.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;



public class Main{
    static long m=998244353l;                   //line 156 modInverse
    static boolean[] vis;                       //line 74 and 91 hasElement ans pth_fnd
    static int MOD=1000000007;
    static int ans=0;
    public static void main(String[] args) throws IOException{
        // long sttm=System.currentTimeMillis();
        FastReader sc=new FastReader();
        OutputStream out=new BufferedOutputStream(System.out);
        int t=sc.nextInt();
        while(t-->0){
            int n=sc.nextInt(),a=sc.nextInt(),b=sc.nextInt(),c=sc.nextInt(),d=sc.nextInt();
            int ll=n*(a-b),lu=n*(a+b);
            int ul=c-d,uu=d+c;
            int x1=ll/ul,x2=lu/uu;
            if((uu<ll || ul>lu)){
                System.out.println("NO");
            }
            else{
                System.out.println("YES");
            }
        }
        out.flush();
        return;
    }



    public static long pow(long n,long k){                 //n-pow(k)
        if(k==1){
            return n%MOD;
        }
        if(k==0){
            return 1;
        }
        long val=pow(n,k/2)%MOD;
        if(k%2==0)return ((val%MOD)*(val%MOD))%MOD;
        else return (((val*val)%MOD)*n)%MOD;
    }


    public static long cnt_sum_k_subar(long[] a,int n,int k){
        HashMap<Long,Long> map=new HashMap<Long,Long>();
        long ret=0;
        long cur_sum=0;
        for(int i=0;i<n;i++){
            cur_sum+=a[i];
            if(cur_sum==k){
                ret++;
            }
            if(map.containsKey(cur_sum-k)){
                ret+=map.get(cur_sum-k);
            }
            if(map.containsKey(cur_sum)){
                map.put(cur_sum, map.get(cur_sum)+1);
            }
            else{
                map.put(cur_sum, (long)1);
            }
        }
        return ret;
    }



    public static ArrayList<Integer> lcm(int num){
        ArrayList<Integer> arrl=new ArrayList<Integer>();
        while(num%2==0){
            arrl.add(2);
            num/=2;
        }
        for(int i=3;i*i<=num;i+=2){
            while(num%i==0){
                arrl.add(i);
                num/=i;
            }
        }
        if(num>2){
            arrl.add(num);
        }
        return arrl;
    }


    static long modInverse(long a,long m) 
    { 
        long m0 = m; 
        long y = 0l, x = 1l; 
  
        if (m == 1) 
            return 0l; 
  
        while (a > 1) 
        { 
  
            long q = a / m; 
  
            long t = m; 
  
            m = a % m; 
            a = t; 
            t = y; 
  
            y = x - q * y; 
            x = t; 
        } 
        if (x < 0) 
            x += m0; 
  
        return x; 
    } 


    public static TreeSet<Long> arr_fact(long num){
        TreeSet<Long> arr=new TreeSet<Long>();
        int cnt=0;
        for(long i=1;i*i<=num;i++){
            if(num%i==0){
                if(i*i==num){
                    cnt+=1;
                    arr.add(i);
                }
                else{
                    arr.add(i);arr.add(num/i);
                    cnt+=2;
                }
            }
        }
        return arr;
    }



    public static int num_fact(int num){
        ArrayList<Integer> arr=new ArrayList<Integer>();
        int cnt=0;
        for(int i=1;i*i<=num;i++){
            if(num%i==0){
                if(i*i==num){
                    cnt+=1;
                }
                else{
                    cnt+=2;
                }
            }
        }
        return cnt;
    }


    public static long cal(int k,int x){
        long val=1;

        for(int i=0;i<k;i++){
            val*=2;
            if(val>x){
                break;
            }
        }
        return val;
    }

    public static void sort_inc(int[][] arr,int col){        //change dimention if req
        Arrays.sort(arr, new Comparator<int[]>() {
            public int compare(final int[] entry1,final int[] entry2) { 
                if (entry1[col] > entry2[col])              //this is for inc
                    return 1; 
                else if(entry1[col]==entry2[col])
                    return 0;
                else
                    return -1; 
            }
        });
    }


    public static boolean prime(int n){
        for(int i=2;i*i<=n;i++){
            if(n%i==0){
                return false;
            }
        }
        return true;
    }


    static long gcd(long a, long b) 
	{ 
	if (b == 0) 
		return a; 
	return gcd(b, a % b); 
	} 
}


class FastReader{ 
    BufferedReader br; 
    StringTokenizer st; 

    public FastReader(){ 
        br = new BufferedReader(new
                 InputStreamReader(System.in)); 
    } 
  
    String next(){ 
        while (st == null || !st.hasMoreElements()){ 
            try{ 
                st = new StringTokenizer(br.readLine()); 
            } 
            catch (IOException  e){ 
                e.printStackTrace(); 
            } 
        } 
        return st.nextToken(); 
    } 
  
    int nextInt(){ 
        return Integer.parseInt(next()); 
    } 
  
    long nextLong(){ 
        return Long.parseLong(next()); 
    }
  
    double nextDouble(){ 
        return Double.parseDouble(next()); 
    }
  
    String nextLine(){ 
        String str = ""; 
        try{ 
            str = br.readLine(); 
        }
        catch (IOException e){ 
            e.printStackTrace(); 
        }
        return str; 
    }
}