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.awt.*;
import java.io.*;
import java.util.StringTokenizer;
import java.util.*;

public class Solution {
    private static final long mod = 1000000007;

    public static void main(String args[]) throws Exception {

        FastScanner sc = new FastScanner();

        int t;
        t = sc.nextInt();
        PrintWriter out = new PrintWriter(System.out);

        while (t-- > 0) {
            solve(sc, out);
        }
        out.close();


    }

    public static void solve(FastScanner sc, PrintWriter out) {
        int n = sc.nextInt();
        int a = sc.nextInt(); int b= sc.nextInt();
        int c = sc.nextInt();
        int d = sc.nextInt();

        long grainMin = a - b; long grainMax = a + b;
        long min = c - d; long max = c + d;
        long minVal = grainMin * n;
        long maxVal = grainMax * n;
        boolean check = false;
        if(minVal < min && maxVal > max)
            check = true;
        if( (minVal <= max && minVal >= min) || (maxVal <= max && maxVal >= min))
        check = true;
if(check)
    out.println("Yes");
else
    out.println("No");
        out.flush();

    }

    public static  <T> void clear(HashMap<Integer,ArrayList<T>> hm){
        for(int key : hm.keySet())
            hm.put(key, new ArrayList<>());
    }

    public static  <T> void fill(HashMap<Integer,ArrayList<T>> hm, int m){
        for(int i = 1;i<=m;i++)
            hm.put(i, new ArrayList<>());
    }



    static long calcChanges(long[] a, long val, int n, long k){
        long ans = 0;
        for(int i = 1;i<=n/2;i++){
            long x = a[i];
            long y = a[n-i-1];
            if((k + x < val && k + y < val) || ( 1 + x > val && 1 + y > val)){
                ans = ans + 2;
            } else if(x + y != val) ans = ans + 1;
        }
        return ans;
    }


    public static class Pair{
        int x;

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Pair)) return false;
            Pair pair = (Pair) o;
            return x == pair.x &&
                    y == pair.y;
        }

        @Override
        public int hashCode() {
            return Objects.hash(x, y);
        }

        int y;
        public static Pair of(int x, int y){
            Pair p = new Pair();
            p.x = x;
            p.y = y;
            return p;
        }
    }



    static class FastScanner {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");

        public String next() {
            while (!st.hasMoreElements())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int[] readArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = nextInt();
            }
            return a;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}



class DFS{


    public void main(String args[]){
        Scanner sc = new Scanner(System.in);
        int n  = sc.nextInt();
        Graph g = new Graph();
        for(int i = 1;i<=n;i++)
            g.addNode(i);

        int e = sc.nextInt();
        while(e-->0){
            int one = sc.nextInt();
            int two = sc.nextInt();
            g.addEdge(one, two);
            g.addEdge(two, one);
        }
        g.resetVisited();
        g.DFS(g.nodes.get(1));


    }
}


class Node{
    int label;
    long touristP;
    long sum;
    Node parent;
    boolean visited = false;
    Node(int l){
        label=l;
        sum = 0;
        touristP = 0;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (!(o instanceof Node)) return false;
        Node node = (Node) o;
        return label == node.label &&
                touristP == node.touristP &&
                sum == node.sum &&
                visited == node.visited;
    }

    @Override
    public int hashCode() {
        return Objects.hash(label);
    }
}

class Graph{

    HashMap<Node,ArrayList<Node>> hm = new HashMap<>();
    HashMap<Integer,Node> nodes = new HashMap<>();
    Graph(){

    }

    void addNode(int n){
        Node node= new Node(n);
        this.nodes.put(n,node);
    }

    void addEdge(int f,int t){
        Node from = nodes.get(f);
        Node to = nodes.get(t);
        if(!hm.containsKey(from))
            hm.put(from,new ArrayList<>());

        hm.get(from).add(to);
    }

    void resetVisited(){
        for(Node n : hm.keySet()){
            n.visited = false;
            for(Node nn:hm.get(n))
                nn.visited = false;
        }
    }

    void DFS(Node n){
        if(n.visited)
            return;

        n.visited = true;
        System.out.print(n.label + " ");
        if(hm.containsKey(n))
            for(Node an : hm.get(n))
                DFS(an);
    }


    long DFSSum(Node n){
        if(n.visited)
            return 0l;

        n.visited = true;
        if(hm.containsKey(n)) {
            for (Node an : hm.get(n)) {
                n.sum = n.sum + DFSSum(an);

            }
        }

        return n.sum+1;
    }

    void BFS(Node n){
        Queue<Node> q = new LinkedList<>();
        q.add(n);

        while(!q.isEmpty()){
            Node node = q.poll();

            System.out.print(node.label+" ");
            node.visited = true;

            if(!hm.containsKey(node))
                continue;

            for(Node nn: hm.get(node)){
                if(nn.visited == false)
                {
                    if(!nn.visited)
                        q.add(nn);
                }
            }
        }

    }
}