Problem: Natasha is going to fly on a rocket to Mars and return to Earth. Also, on the way to Mars, she will land on n - 2 intermediate planets. Formally: we number all the planets from 1 to n. 1 is Earth, n is Mars. Natasha will make exactly n flights: 1 → 2 → … n → 1.

Flight from x to y consists of two phases: take-off from planet x and landing to planet y. This way, the overall itinerary of the trip will be: the 1-st planet → take-off from the 1-st planet → landing to the 2-nd planet → 2-nd planet → take-off from the 2-nd planet → … → landing to the n-th planet → the n-th planet → take-off from the n-th planet → landing to the 1-st planet → the 1-st planet.

The mass of the rocket together with all the useful cargo (but without fuel) is m tons. However, Natasha does not know how much fuel to load into the rocket. Unfortunately, fuel can only be loaded on Earth, so if the rocket runs out of fuel on some other planet, Natasha will not be able to return home. Fuel is needed to take-off from each planet and to land to each planet. It is known that 1 ton of fuel can lift off a_i tons of rocket from the i-th planet or to land b_i tons of rocket onto the i-th planet. 

For example, if the weight of rocket is 9 tons, weight of fuel is 3 tons and take-off coefficient is 8 (a_i = 8), then 1.5 tons of fuel will be burnt (since 1.5 ⋅ 8 = 9 + 3). The new weight of fuel after take-off will be 1.5 tons. 

Please note, that it is allowed to burn non-integral amount of fuel during take-off or landing, and the amount of initial fuel can be non-integral as well.

Help Natasha to calculate the minimum mass of fuel to load into the rocket. Note, that the rocket must spend fuel to carry both useful cargo and the fuel itself. However, it doesn't need to carry the fuel which has already been burnt. Assume, that the rocket takes off and lands instantly.

Input

The first line contains a single integer n (2 ≤ n ≤ 1000) — number of planets.

The second line contains the only integer m (1 ≤ m ≤ 1000) — weight of the payload.

The third line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 1000), where a_i is the number of tons, which can be lifted off by one ton of fuel.

The fourth line contains n integers b_1, b_2, …, b_n (1 ≤ b_i ≤ 1000), where b_i is the number of tons, which can be landed by one ton of fuel. 

It is guaranteed, that if Natasha can make a flight, then it takes no more than 10^9 tons of fuel.

Output

If Natasha can fly to Mars through (n - 2) planets and return to Earth, print the minimum mass of fuel (in tons) that Natasha should take. Otherwise, print a single number -1.

It is guaranteed, that if Natasha can make a flight, then it takes no more than 10^9 tons of fuel.

The answer will be considered correct if its absolute or relative error doesn't exceed 10^{-6}. Formally, let your answer be p, and the jury's answer be q. Your answer is considered correct if \frac{|p - q|}{max{(1, |q|)}} ≤ 10^{-6}.

Examples

Input

2
12
11 8
7 5


Output

10.0000000000


Input

3
1
1 4 1
2 5 3


Output

-1


Input

6
2
4 6 3 3 5 6
2 6 3 6 5 3


Output

85.4800000000

Note

Let's consider the first example.

Initially, the mass of a rocket with fuel is 22 tons.

  * At take-off from Earth one ton of fuel can lift off 11 tons of cargo, so to lift off 22 tons you need to burn 2 tons of fuel. Remaining weight of the rocket with fuel is 20 tons.
  * During landing on Mars, one ton of fuel can land 5 tons of cargo, so for landing 20 tons you will need to burn 4 tons of fuel. There will be 16 tons of the rocket with fuel remaining.
  * While taking off from Mars, one ton of fuel can raise 8 tons of cargo, so to lift off 16 tons you will need to burn 2 tons of fuel. There will be 14 tons of rocket with fuel after that.
  * During landing on Earth, one ton of fuel can land 7 tons of cargo, so for landing 14 tons you will need to burn 2 tons of fuel. Remaining weight is 12 tons, that is, a rocket without any fuel.



In the second case, the rocket will not be able even to take off from Earth.

Solution (in JAVA):

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

public class tr1 {
	static PrintWriter out;
	static StringBuilder sb;
	static int inf = (int) 1e9;
	static long mod = (long) 998244353;
	static int[] si;
	static ArrayList<Integer> primes;
	static HashSet<Integer> pr;
	static int n, k, m;
	static int[] in;
	static HashMap<Integer, Integer> factors;
	static HashSet<Integer> f;
	static int[] fac, a, b;
	static int[] l, r;
	static int[][] memo;
	static int[] numc;
	static ArrayList<Integer>[] ad;
	static HashMap<Integer, Integer> hm;
	static pair[] ed;
	static TreeSet<Integer>[] np;
	static TreeMap<pair, Integer> tm;
	static int[] le, re;
	static char[] h;
	static pair[] mm;
	static boolean[] vis;
	static int y;

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		out = new PrintWriter(System.out);
		int n = sc.nextInt();
		double m = sc.nextInt();
		double[] up = new double[n];
		double[] land = new double[n];
		double lo = 0;
		double hi = 1e9+3;
		for(int i=0;i<n;i++) {
			up[i]=sc.nextDouble();
			land[i]=sc.nextDouble();
		}
		int c = 0;
		double ans = -1;
		while (lo <= hi) {
			if (c == 200)
				break;
			c++;
			double mid = (lo + hi) / 2d;
			boolean f = true;
			double total=mid+m;
			double le=mid;
			le-=total/up[0];
			total-=total/up[0];
			for(int i=1;i<n;i++) {
				if(le<=0)
					f=false;
				le-=total/land[i];
				total-=total/land[i];
				le-=total/up[i];
				total-=total/up[i];
			}
			le-=total/land[0];
			total-=total/land[0];
			if(le<0)
				f=false;
		//	System.out.println(mid+" "+lo+" "+hi+" "+f+" "+le);
			if (f) {
                 ans=mid;
                 hi=mid;
			} else {
                   lo=mid;
			}
		}
		if (ans == -1)
			out.print(-1);
		else
			out.print(ans);
		out.flush();
	}

	static class pair implements Comparable<pair> {
		int node;
		int level;

		pair(int f, int t) {
			node = t;
			level = f;
		}

		public String toString() {
			return node + " " + level;
		}

		@Override
		public int compareTo(pair o) {
			return level - o.level;
		}
	}

	static class pair1 implements Comparable<pair1> {
		int x;
		int y;
		int z;

		pair1(int f, int t, int u) {
			x = f;
			y = t;
			z = u;
			// num = n;
		}

		public String toString() {
			return x + " " + y;
		}

		@Override
		public int compareTo(pair1 o) {
			if (x == o.x)
				return y - o.y;
			return x - o.x;
		}
	}

	static public class FenwickTree { // one-based DS

		int n;
		int[] ft;

		FenwickTree(int size) {
			n = size;
			ft = new int[n + 1];
			// for(int i=1;i<=n;i++)
			// ft[i]=i;
		}

		int rsq(int b) // O(log n)
		{
			int sum = 0;
			while (b > 0) {
				sum += ft[b];
				b -= b & -b;
			} // min?
			return sum;
		}

		int rsq(int a, int b) {
			return rsq(b) - rsq(a - 1);
		}

		void point_update(int k, int val) // O(log n), update = increment
		{
			while (k <= n) {
				// System.out.println(k+" "+val);
				ft[k] += val;
				k += k & -k;
			} // min?
		}

		int point_query(int idx) // c * O(log n), c < 1
		{
			int sum = ft[idx];
			if (idx > 0) {
				int z = idx ^ (idx & -idx);
				--idx;
				while (idx != z) {
					// System.out.println("oo");
					sum -= ft[idx];
					idx ^= idx & -idx;
				}
			}
			return sum;
		}

		void scale(int c) {
			for (int i = 1; i <= n; ++i)
				ft[i] *= c;
		}

		int findIndex(int cumFreq) {
			int msk = n;
			while ((msk & (msk - 1)) != 0)
				msk ^= msk & -msk; // msk will contain the MSB of n

			int idx = 0;
			while (msk != 0) {
				int tIdx = idx + msk;
				if (tIdx <= n && cumFreq >= ft[tIdx]) {
					idx = tIdx;
					cumFreq -= ft[tIdx];
				}
				msk >>= 1;
			}
			if (cumFreq != 0)
				return -1;
			return idx;
		}
	}

	static public class SegmentTree { // 1-based DS, OOP

		int N; // the number of elements in the array as a power of 2 (i.e. after padding)
		long[] array, sTree, lazy;

		SegmentTree(long[] in) {
			array = in;
			N = in.length - 1;
			sTree = new long[N << 1]; // no. of nodes = 2*N - 1, we add one to cross out index zero
			lazy = new long[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, long 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, long 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;
		}

		long query(int i, int j) {
			return query(1, 1, N, i, j);
		}

		long 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);
			long q1 = query(node << 1, b, mid, i, j);
			long q2 = query(node << 1 | 1, mid + 1, e, i, j);
			return q1 + q2;

		}

	}

	static long gcd(long a, long b) {

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

	public int[] merge(int[] d, int st, int e) {
		if (st > e)
			return null;
		if (e == st) {
			int[] ans = { d[e] };
			return ans;
		}
		int mid = (st + e) / 2;
		int[] ans = new int[e - st + 1];
		int[] ll = merge(d, st, mid);
		int[] rr = merge(d, mid + 1, e);
		if (ll == null)
			return rr;
		if (rr == null)
			return ll;
		int iver = 0;
		int idxl = 0;
		int idxr = 0;
		for (int i = st; i <= e; i++) {
			if (ll[idxl] < rr[idxr]) {

			}
		}
		return ans;
	}

	public static class pair2 implements Comparable<pair2> {
		int a;
		int idx;

		pair2(int a, int i) {
			this.a = a;
			idx = i;
		}

		public String toString() {
			return a + " " + idx;
		}

		@Override
		public int compareTo(pair2 o) {
			// TODO Auto-generated method stub
			return idx - o.idx;
		}
	}

	static long inver(long x) {
		int a = (int) x;
		long e = (mod - 2);
		long res = 1;
		while (e > 0) {
			if ((e & 1) == 1) {
				// System.out.println(res*a);
				res = (int) ((1l * res * a) % mod);
			}
			a = (int) ((1l * a * a) % mod);
			e >>= 1;
		}
		// out.println(res+" "+x);
		return res % mod;
	}

	static int atMostSum(int arr[], int n, int k) {
		int sum = 0;
		int cnt = 0, maxcnt = 0;

		for (int i = 0; i < n; i++) {

			// If adding current element doesn't
			// cross limit add it to current window
			if ((sum + arr[i]) <= k) {
				sum += arr[i];
				cnt++;
			}

			// Else, remove first element of current
			// window and add the current element
			else if (sum != 0) {
				sum = sum - arr[i - cnt] + arr[i];
			}

			// keep track of max length.
			maxcnt = Math.max(cnt, maxcnt);
		}
		return maxcnt;
	}

	public static int[] longestSubarray(int[] inp) {
		// array containing prefix sums up to a certain index i
		int[] p = new int[inp.length];
		p[0] = inp[0];
		for (int i = 1; i < inp.length; i++) {
			p[i] = p[i - 1] + inp[i];
		}

		// array Q from the description below
		int[] q = new int[inp.length];
		q[inp.length - 1] = p[inp.length - 1];
		for (int i = inp.length - 2; i >= 0; i--) {
			q[i] = Math.max(q[i + 1], p[i]);
		}
		int a = 0;
		int b = 0;
		int maxLen = 0;
		int curr;
		int[] res = new int[] { -1, -1 };
		while (b < inp.length) {
			curr = a > 0 ? q[b] - p[a - 1] : q[b];
			if (curr >= 0) {
				if (b - a > maxLen) {
					maxLen = b - a;
					res = new int[] { a, b };
				}
				b++;
			} else {
				a++;
			}
		}
		return res;
	}

	static void factor(int n) {
		if (si[n] == n) {
			f.add(n);
			return;
		}
		f.add(si[n]);
		factor(n / si[n]);
	}

	static void seive() {
		si = new int[100001];
		primes = new ArrayList<>();
		int N = 100001;
		si[1] = 1;
		for (int i = 2; i < N; i++) {
			if (si[i] == 0) {
				si[i] = i;
				primes.add(i);
			}
			for (int j = 0; j < primes.size() && primes.get(j) <= si[i] && (i * primes.get(j)) < N; j++)
				si[primes.get(j) * i] = primes.get(j);

		}
	}

	static class unionfind {
		int[] p;
		int[] size;
		int jum;

		unionfind(int n) {
			p = new int[n];
			size = new int[n];

			for (int i = 0; i < n; i++) {
				p[i] = i;
			}
			jum = n;
			Arrays.fill(size, 1);
		}

		int findSet(int v) {
			if (v == p[v])
				return v;
			return p[v] = findSet(p[v]);
		}

		boolean sameSet(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return true;
			return false;
		}

		int max() {
			int max = 0;
			for (int i = 0; i < size.length; i++)
				if (size[i] > max)
					max = size[i];
			return max;
		}

		void combine(int a, int b) {
			a = findSet(a);
			b = findSet(b);
			if (a == b)
				return;
			jum--;
			if (size[a] > size[b]) {
				p[b] = a;
				size[a] += size[b];

			} else {
				p[a] = b;
				size[b] += size[a];
			}
		}
	}

	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);
		}
	}
}