Problem: Creatnx has n mirrors, numbered from 1 to n. Every day, Creatnx asks exactly one mirror "Am I beautiful?". The i-th mirror will tell Creatnx that he is beautiful with probability (p_i)/(100) for all 1 ≤ i ≤ n.

Some mirrors are called checkpoints. Initially, only the 1st mirror is a checkpoint. It remains a checkpoint all the time.

Creatnx asks the mirrors one by one, starting from the 1-st mirror. Every day, if he asks i-th mirror, there are two possibilities:

  * The i-th mirror tells Creatnx that he is beautiful. In this case, if i = n Creatnx will stop and become happy, otherwise he will continue asking the i+1-th mirror next day; 
  * In the other case, Creatnx will feel upset. The next day, Creatnx will start asking from the checkpoint with a maximal number that is less or equal to i. 



There are some changes occur over time: some mirrors become new checkpoints and some mirrors are no longer checkpoints. You are given q queries, each query is represented by an integer u: If the u-th mirror isn't a checkpoint then we set it as a checkpoint. Otherwise, the u-th mirror is no longer a checkpoint.

After each query, you need to calculate [the expected number](https://en.wikipedia.org/wiki/Expected_value) of days until Creatnx becomes happy.

Each of this numbers should be found by modulo 998244353. Formally, let M = 998244353. It can be shown that the answer can be expressed as an irreducible fraction p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output the integer equal to p ⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.

Input

The first line contains two integers n, q (2 ≤ n, q ≤ 2 ⋅ 10^5) — the number of mirrors and queries.

The second line contains n integers: p_1, p_2, …, p_n (1 ≤ p_i ≤ 100).

Each of q following lines contains a single integer u (2 ≤ u ≤ n) — next query.

Output

Print q numbers – the answers after each query by modulo 998244353.

Examples

Input


2 2
50 50
2
2


Output


4
6


Input


5 5
10 20 30 40 50
2
3
4
5
3


Output


117
665496274
332748143
831870317
499122211

Note

In the first test after the first query, the first and the second mirrors are checkpoints. Creatnx will ask the first mirror until it will say that he is beautiful, after that he will ask the second mirror until it will say that he is beautiful because the second mirror is a checkpoint. After that, he will become happy. Probabilities that the mirrors will say, that he is beautiful are equal to 1/2. So, the expected number of days, until one mirror will say, that he is beautiful is equal to 2 and the answer will be equal to 4 = 2 + 2.

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.Closeable;
import java.io.DataInputStream;
import java.io.Flushable;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.InputMismatchException;
import java.util.Objects;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	static class TaskAdapter implements Runnable {
		@Override
		public void run() {
			InputStream inputStream = System.in;
			OutputStream outputStream = System.out;
			FastReader in = new FastReader(inputStream);
			Output out = new Output(outputStream);
			EBeautifulMirrors solver = new EBeautifulMirrors();
			solver.solve(1, in, out);
			out.close();
		}
	}

	public static void main(String[] args) throws Exception {
		Thread thread = new Thread(null, new TaskAdapter(), "", 1<<28);
		thread.start();
		thread.join();
	}

	static class EBeautifulMirrors {
		private final int mod = 998244353;

		public EBeautifulMirrors() {
		}

		public void solve(int kase, InputReader in, Output pw) {
			int n = in.nextInt();
			Fraction b = new Fraction(0), one = new Fraction(1);
			for(int i = 0; i<n; i++) {
				Fraction a = new Fraction(in.nextInt(), 100);
				b = a.multiply(b.opposite()).subtract(a).add(b).add(one).divide(a);
				b = new Fraction(b.num%mod, b.den%mod);
			}
			pw.println((b.num*Utilities.math.pow(b.den, mod-2, mod))%mod);
		}

	}

	static class Utilities {
		public static long gcd(long a, long b) {
			return b==0 ? a : gcd(b, a%b);
		}

		public static class math {
			public static long pow(long base, long exp, long mod) {
				long ans = 1, cur = base;
				while(exp>0) {
					if((exp&1)>0) {
						ans = (ans*cur)%mod;
					}
					cur = (cur*cur)%mod;
					exp >>= 1;
				}
				return ans;
			}

		}

	}

	static interface InputReader {
		int nextInt();

	}

	static final class Fraction implements Comparable<Fraction> {
		public long num;
		public long den;

		public Fraction(Fraction f) {
			num = f.num;
			den = f.den;
		}

		public Fraction(long numerator, long denominator) {
			num = numerator;
			den = denominator;
			simplify();
		}

		public Fraction(long value) {
			num = value;
			den = 1;
		}

		public boolean equals(Object o) {
			if(this==o) return true;
			if(o==null||getClass()!=o.getClass()) return false;
			Fraction f = (Fraction) o;
			return num*f.den==
					den*f.num;
		}

		public int hashCode() {
			return Objects.hash(num, den);
		}

		public String toString() {
			return num+"/"+den;
		}

		public int compareTo(Fraction f) {
			return Long.compare(num*f.den, den*f.num);
		}

		public void simplify() {
			long gcd = Utilities.gcd(num, den);
			num /= gcd;
			den /= gcd;
		}

		public Fraction multiply(Fraction f) {
			Fraction ret = new Fraction(num*f.num, den*f.den);
			ret.simplify();
			return ret;
		}

		public Fraction divide(Fraction f) {
			return multiply(f.reciprocal());
		}

		public Fraction add(Fraction f) {
			Fraction ret = new Fraction(num*f.den+den*f.num, den*f.den);
			ret.simplify();
			return ret;
		}

		public Fraction subtract(Fraction f) {
			return add(opposite());
		}

		public Fraction reciprocal() {
			return new Fraction(den, num);
		}

		public Fraction opposite() {
			return new Fraction(-num, den);
		}

	}

	static class FastReader implements InputReader {
		final private int BUFFER_SIZE = 1<<16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer;
		private int bytesRead;

		public FastReader(InputStream is) {
			din = new DataInputStream(is);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public int nextInt() {
			int ret = 0;
			byte c = skipToDigit();
			boolean neg = (c=='-');
			if(neg) {
				c = read();
			}
			do {
				ret = ret*10+c-'0';
			} while((c = read())>='0'&&c<='9');
			if(neg) {
				return -ret;
			}
			return ret;
		}

		private boolean isDigit(byte b) {
			return b>='0'&&b<='9';
		}

		private byte skipToDigit() {
			byte ret;
			while(!isDigit(ret = read())&&ret!='-') ;
			return ret;
		}

		private void fillBuffer() {
			try {
				bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			}catch(IOException e) {
				e.printStackTrace();
				throw new InputMismatchException();
			}
			if(bytesRead==-1) {
				buffer[0] = -1;
			}
		}

		private byte read() {
			if(bytesRead==-1) {
				throw new InputMismatchException();
			}else if(bufferPointer==bytesRead) {
				fillBuffer();
			}
			return buffer[bufferPointer++];
		}

	}

	static class Output implements Closeable, Flushable {
		public StringBuilder sb;
		public OutputStream os;
		public int BUFFER_SIZE;
		public String lineSeparator;

		public Output(OutputStream os) {
			this(os, 1<<16);
		}

		public Output(OutputStream os, int bs) {
			BUFFER_SIZE = bs;
			sb = new StringBuilder(BUFFER_SIZE);
			this.os = new BufferedOutputStream(os, 1<<17);
			lineSeparator = System.lineSeparator();
		}

		public void println(long l) {
			println(String.valueOf(l));
		}

		public void println(String s) {
			sb.append(s);
			println();
		}

		public void println() {
			sb.append(lineSeparator);
		}

		private void flushToBuffer() {
			try {
				os.write(sb.toString().getBytes());
			}catch(IOException e) {
				e.printStackTrace();
			}
			sb = new StringBuilder(BUFFER_SIZE);
		}

		public void flush() {
			try {
				flushToBuffer();
				os.flush();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

		public void close() {
			flush();
			try {
				os.close();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

	}
}