import std.conv, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.container, std.math, std.numeric, std.range, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } void chmin(T)(ref T t, in T f) { if (t > f) t = f; } void chmax(T)(ref T t, in T f) { if (t < f) t = f; } int binarySearch(T)(in T[] as, in bool delegate(T) test) { int low = -1, upp = cast(int)(as.length); for (; low + 1 < upp; ) { int mid = (low + upp) >> 1; (test(as[mid]) ? low : upp) = mid; } return upp; } int lowerBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a < val)); } int upperBound(T)(in T[] as, in T val) { return as.binarySearch((T a) => (a <= val)); } int M, N; real[][] P; int[][] S; void main() { try { for (; ; ) { M = readInt(); N = readInt(); P = new real[][](M, N); foreach (x; 0 .. M) foreach (y; 0 .. N) { P[x][y] = readInt() / 100.0; } S = new int[][](M, N); foreach (x; 0 .. M) foreach (y; 0 .. N) { S[x][y] = readInt(); } auto prob = new real[][](M, 1 << N); foreach (x; 0 .. M) { foreach (a; 0 .. 1 << N) { prob[x][a] = 1.0; foreach (y; 0 .. N) { prob[x][a] *= ((a >> y) & 1) ? P[x][y] : (1.0 - P[x][y]); } } } auto trans = new int[1 << (N * 2)]; foreach (key; 0 .. 1 << (N * 2)) { int bb; foreach (y; 0 .. N) { if (((key >> (y * 2)) & 3) + ((bb << 1 >> y) & 1) + ((bb >> (y + 1)) & 1) >= 3) { bb |= 1 << y; } } foreach_reverse (y; 0 .. N) { if (((key >> (y * 2)) & 3) + ((bb << 1 >> y) & 1) + ((bb >> (y + 1)) & 1) >= 3) { bb |= 1 << y; } } trans[key] = bb; debug{ if(N==2)writefln("trans[%04b] = %02b",key,bb); } } auto mask = new int[1 << N]; foreach (a; 0 .. 1 << N) { foreach (y; 0 .. N) { if ((a >> y) & 1) { mask[a] |= 3 << (y * 2); } } } auto dp = new real[][](M + 1, 1 << N); foreach (x; 0 .. M + 1) { dp[x][] = 0.0; } dp[0][0] = 1.0; foreach (x; 0 .. M) { foreach (b; 0 .. 1 << N) { if (isNormal(dp[x][b])) { int key; auto s = new int[N]; foreach (y; 0 .. N) { key |= min(max(-1 + (4 - S[x][y]) + ((b >> y) & 1), 0), 3) << (y * 2); } foreach (a; 0 .. 1 << N) { const bb = trans[key & mask[a]]; debug{ if(N==2)writefln("x = %s, b = %02b: key = %04b; a = %02b: bb = %02b",x,b,key,a,bb); } dp[x + 1][bb] += dp[x][b] * prob[x][a]; } } } } real ans = 0.0; foreach (x; 0 .. M) { foreach (b; 0 .. 1 << N) { ans += dp[x + 1][b] * popcnt(b); } } writefln("%.20f", ans); } } catch (EOFException e) { } }