Problem: Ivan is going to sleep now and wants to set his alarm clock. There will be many necessary events tomorrow, the i-th of them will start during the x_i-th minute. Ivan doesn't want to skip any of the events, so he has to set his alarm clock in such a way that it rings during minutes x_1, x_2, ..., x_n, so he will be awake during each of these minutes (note that it does not matter if his alarm clock will ring during any other minute).

Ivan can choose two properties for the alarm clock — the first minute it will ring (let's denote it as y) and the interval between two consecutive signals (let's denote it by p). After the clock is set, it will ring during minutes y, y + p, y + 2p, y + 3p and so on.

Ivan can choose any minute as the first one, but he cannot choose any arbitrary value of p. He has to pick it among the given values p_1, p_2, ..., p_m (his phone does not support any other options for this setting).

So Ivan has to choose the first minute y when the alarm clock should start ringing and the interval between two consecutive signals p_j in such a way that it will ring during all given minutes x_1, x_2, ..., x_n (and it does not matter if his alarm clock will ring in any other minutes).

Your task is to tell the first minute y and the index j such that if Ivan sets his alarm clock with properties y and p_j it will ring during all given minutes x_1, x_2, ..., x_n or say that it is impossible to choose such values of the given properties. If there are multiple answers, you can print any.

Input

The first line of the input contains two integers n and m (2 ≤ n ≤ 3 ⋅ 10^5, 1 ≤ m ≤ 3 ⋅ 10^5) — the number of events and the number of possible settings for the interval between signals.

The second line of the input contains n integers x_1, x_2, ..., x_n (1 ≤ x_i ≤ 10^{18}), where x_i is the minute when i-th event starts. It is guaranteed that all x_i are given in increasing order (i. e. the condition x_1 < x_2 < ... < x_n holds).

The third line of the input contains m integers p_1, p_2, ..., p_m (1 ≤ p_j ≤ 10^{18}), where p_j is the j-th option for the interval between two consecutive signals.

Output

If it's impossible to choose such values y and j so all constraints are satisfied, print "NO" in the first line.

Otherwise print "YES" in the first line. Then print two integers y (1 ≤ y ≤ 10^{18}) and j (1 ≤ j ≤ m) in the second line, where y is the first minute Ivan's alarm clock should start ringing and j is the index of the option for the interval between two consecutive signals (options are numbered from 1 to m in the order they are given input). These values should be chosen in such a way that the alarm clock will ring during all given minutes x_1, x_2, ..., x_n. If there are multiple answers, you can print any.

Examples

Input


3 5
3 12 18
2 6 5 3 3


Output


YES
3 4


Input


4 2
1 5 17 19
4 5


Output


NO


Input


4 2
1 5 17 19
2 1


Output


YES
1 1

Solution (in JAVA):

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


public class Main_1155C {

	private static Scanner sc;
	private static Printer pr;

	private static void solve() {
		int n = sc.nextInt();
		int m = sc.nextInt();
		long[] x = sc.nextLongArray(n);
		long[] p = sc.nextLongArray(m);

		long gcd = x[1] - x[0];
		for (int i = 1; i < n; i++) {
			gcd = gcd(gcd, x[i] - x[i - 1]);
		}

		for (int i = 0; i < m; i++) {
			if (gcd % p[i] == 0) {
				pr.println("YES");
				pr.printf("%d %d%n", x[0], i + 1);
				return;
			}
		}
		
		pr.println("NO");
	}

	static long gcd(long n, long m) {
		if (m == 0) {
			return n;
		} else {
			return gcd(m, n % m);
		}
	}

	// ---------------------------------------------------
	public static void main(String[] args) {
		sc = new Scanner(System.in);
		pr = new Printer(System.out);
			
		solve();
			
		pr.close();
		sc.close();
	}

	static class Scanner {
		BufferedReader br;

		Scanner (InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}

		private boolean isPrintable(int ch) {
			return ch >= '!' && ch <= '~';
		}

		private boolean isCRLF(int ch) {
			return ch == '\n' || ch == '\r' || ch == -1;
		}

		private int nextPrintable() {
			try {
				int ch;
				while (!isPrintable(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}

				return ch;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		String next() {
			try {
				int ch = nextPrintable();
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (isPrintable(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		int nextInt() {
			try {
				// parseInt from Integer.parseInt()
				boolean negative = false;
				int res = 0;
				int limit = -Integer.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Integer.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				int multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		long nextLong() {
			try {
				// parseLong from Long.parseLong()
				boolean negative = false;
				long res = 0;
				long limit = -Long.MAX_VALUE;
				int radix = 10;

				int fc = nextPrintable();
				if (fc < '0') {
					if (fc == '-') {
						negative = true;
						limit = Long.MIN_VALUE;
					} else if (fc != '+') {
						throw new NumberFormatException();
					}
					fc = br.read();
				}
				long multmin = limit / radix;

				int ch = fc;
				do {
					int digit = ch - '0';
					if (digit < 0 || digit >= radix) {
						throw new NumberFormatException();
					}
					if (res < multmin) {
						throw new NumberFormatException();
					}
					res *= radix;
					if (res < limit + digit) {
						throw new NumberFormatException();
					}
					res -= digit;

				} while (isPrintable(ch = br.read()));

				return negative ? res : -res;
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}

		float nextFloat() {
			return Float.parseFloat(next());
		}

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

		String nextLine() {
			try {
				int ch;
				while (isCRLF(ch = br.read())) {
					if (ch == -1) {
						throw new NoSuchElementException();
					}
				}
				StringBuilder sb = new StringBuilder();
				do {
					sb.appendCodePoint(ch);
				} while (!isCRLF(ch = br.read()));

				return sb.toString();
			} catch (IOException e) {
				throw new NoSuchElementException();
			}
		}
		
		int[] nextIntArray(int n) {
			int[] ret = new int[n];
			for (int i = 0; i < n; i++) {
				ret[i] = sc.nextInt();
			}
			
			return ret;
		}

		long[] nextLongArray(int n) {
			long[] ret = new long[n];
			for (int i = 0; i < n; i++) {
				ret[i] = sc.nextLong();
			}
			
			return ret;
		}

		int[][] nextIntArrays(int n, int m) {
			int[][] ret = new int[m][n];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					ret[j][i] = sc.nextInt();
				}
			}
			
			return ret;
		}

		void close() {
			try {
				br.close();
			} catch (IOException e) {
//				throw new NoSuchElementException();
			}
		}
	}

	static class Printer extends PrintWriter {
		Printer(OutputStream out) {
			super(out);
		}
		
		void printInts(int... a) {
			StringBuilder sb = new StringBuilder(32);
			for (int i = 0, size = a.length; i < size; i++) {
				if (i > 0) {
					sb.append(' ');
				}
				sb.append(a[i]);
			}

			println(sb);
		}
		
		void printLongs(long... a) {
			StringBuilder sb = new StringBuilder(64);
			for (int i = 0, size = a.length; i < size; i++) {
				if (i > 0) {
					sb.append(' ');
				}
				sb.append(a[i]);
			}

			println(sb);
		}
		
		void printStrings(String... a) {
			StringBuilder sb = new StringBuilder(32);
			for (int i = 0, size = a.length; i < size; i++) {
				if (i > 0) {
					sb.append(' ');
				}
				sb.append(a[i]);
			}

			println(sb);
		}
	}
}