import java.io.BufferedReader; import java.io.IOException; import java.io.InputStream; import java.io.InputStreamReader; import java.util.Arrays; import java.util.HashSet; import java.util.LinkedList; import java.util.Scanner; import java.util.Set; import java.util.StringTokenizer; public class Main { public static final double EPS = 1e-8; public static void main(String[] args) { Scanner sc = new Scanner(System.in); final int R = sc.nextInt(); final int C = sc.nextInt(); double[][] probs = new double[R][C]; for(int i = 0; i < R; i++){ for(int j = 0; j < C; j++){ probs[i][j] = sc.nextDouble(); } } int[][] shys = new int[R][C]; for(int i = 0; i < R; i++){ for(int j = 0; j < C; j++){ shys[i][j] = sc.nextInt(); } } final int DP_SIZE = 1 << C; double[][] knowns_probs = new double[R][DP_SIZE]; for(int r = 0; r < R; r++){ Arrays.fill(knowns_probs[r], 1); } int[] shy_zero_bits = new int[R]; int[] shy_one_bits = new int[R]; for(int r = 0; r < R; r++){ for(int c = 0; c < C; c++){ shy_zero_bits[r] |= (((shys[r][c] == 0) ? 1 : 0) << c); shy_one_bits[r] |= (((shys[r][c] == 1) ? 1 : 0) << c); } } for(int bit = 0; bit < DP_SIZE; bit++){ for(int r = 0; r < R; r++){ for(int i = 0; i < C; i++){ knowns_probs[r][bit] *= ((bit & (1 << i)) != 0) ? (probs[r][i] / 100.0) : (1 - probs[r][i] / 100.0); } } } double[][] DP = new double[R + 1][DP_SIZE]; //配るDPする. boolean[][] reached = new boolean[R + 1][DP_SIZE]; Arrays.fill(DP[0], 0); DP[0][0] = 1.0; reached[0][0] = true; int[] curr_line = new int[C]; for(int r = 0; r < R; r++){ // O(R) -> 11 //System.out.println(r); for(int prev_raise_bit = 0; prev_raise_bit < DP_SIZE; prev_raise_bit++){ // O(R * 2^C) -> if(!reached[r][prev_raise_bit]){ continue; } final int somebody_raise_bit = shy_zero_bits[r] | (shy_one_bits[r] & prev_raise_bit); for(int curr_known_bit = 0; curr_known_bit < DP_SIZE; curr_known_bit++) { // O(R * 2^C * 2^C) -> if((curr_known_bit & somebody_raise_bit) == 0){ DP[r + 1][0] += DP[r][prev_raise_bit] * knowns_probs[r][curr_known_bit]; reached[r + 1][0] |= true; continue; } int curr_raise_bit = 0; for(int i = 0; i < C; i++){ curr_line[i] = ((curr_known_bit & (1 << i)) == 0 ? 0 : 4 - shys[r][i]) + ((prev_raise_bit & (1 << i)) != 0 ? 1 : 0); if(curr_line[i] >= 4){ curr_raise_bit |= (1 << i); }; } for(int i = 0; i < C - 1; i++){ if((curr_raise_bit & (1 << i)) != 0 && (curr_raise_bit & (1 << (i + 1))) == 0){ if(++curr_line[i + 1] >= 4){ curr_raise_bit |= (1 << (i + 1)); } } } for(int i = C - 1; i >= 1; i--){ if((curr_raise_bit & (1 << i)) != 0 && (curr_raise_bit & (1 << (i - 1))) == 0){ if(++curr_line[i - 1] >= 4){ curr_raise_bit |= (1 << (i - 1)); } } } DP[r + 1][curr_raise_bit] += DP[r][prev_raise_bit] * knowns_probs[r][curr_known_bit]; reached[r + 1][curr_raise_bit] |= true; } } } /* for(double[] bits : DP){ System.out.println(Arrays.toString(bits)); } */ double answer = 0; for(int r = 1; r <= R; r++){ for(int bit = 0; bit < DP_SIZE; bit++){ answer += Integer.bitCount(bit) * DP[r][bit]; } } System.out.printf("%.11f\n", answer); } public static class Scanner { private BufferedReader br; private StringTokenizer tok; public Scanner(InputStream is) { br = new BufferedReader(new InputStreamReader(is)); } private void getLine() { try { while (!hasNext()) {tok = new StringTokenizer(br.readLine());} } catch(IOException e){ /* ignore */ } } private boolean hasNext() { return tok != null && tok.hasMoreTokens(); } public String next() { getLine(); return tok.nextToken(); } public int nextInt(){ return Integer.parseInt(next()); } public double nextDouble(){ return Double.parseDouble(next()); } public void close() { try{ br.close(); } catch (IOException e){ /*ignore*/ } } } }