import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, 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; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } void main() { try { for (; ; ) { const N = readInt(); const X = readInt(); auto A = new int[N]; foreach (i; 0 .. N) { A[i] = readInt(); } A.sort; long prod = 1; foreach (i; 0 .. N) { prod *= (A[i] + 1); if (prod - 1 > X) { foreach (x; 1 .. X + 1) { write(0); } writeln(); goto failed; } } { const grp = A.group.array; const m = cast(int)(grp.length); debug { writeln("grp = ", grp); } int encode(int[] as) { int key; foreach_reverse (j; 0 .. m) { key = key * (grp[j][1] + 1) + as[j]; } return key; } int[] decode(int key) { auto as = new int[m]; foreach (j; 0 .. m) { as[j] = key % (grp[j][1] + 1); key /= (grp[j][1] + 1); } return as; } int V = 1; foreach (j; 0 .. m) { V *= (grp[j][1] + 1); } auto prods = new int[V]; foreach (u; 0 .. V) { const as = decode(u); prods[u] = 1; foreach (j; 0 .. m) { prods[u] *= (grp[j][0] + 1)^^as[j]; } } auto lbs = new int[V]; auto ubs = new int[V]; foreach (u; 0 .. V) { const as = decode(u); lbs[u] = prods[u] - 1; ubs[u] = (X + 1) / prods[V - 1 - u] - 1 + 1; } auto dp = new int[][V]; foreach (u; 1 .. V) { const as = decode(u); dp[u] = [lbs[u]]; void dfs(int j, int[] bs, int[] cs) { if (j == m) { const v = encode(bs); const w = encode(cs); if (v != 0 && w != 0 && v <= w) { foreach (x; dp[v]) foreach (y; dp[w]) { for (int z = (x + 1) * (y + 1) - 1; z < ubs[u]; z += x) { dp[u] ~= z; } for (int z = (x + 1) * (y + 1) - 1; z < ubs[u]; z += y) { dp[u] ~= z; } } } return; } for (bs[j] = 0; bs[j] <= as[j]; ++bs[j]) { cs[j] = as[j] - bs[j]; dfs(j + 1, bs, cs); } } dfs(0, new int[m], new int[m]); dp[u] = dp[u].sort.uniq.array; debug { writeln(u, " ", as, ": ", prods[u], " ", lbs[u], " ", ubs[u], " ", dp[u]); } } auto ans = new char[X + 1]; ans[] = '0'; foreach (x; dp[V - 1]) { ans[x] = '1'; } writeln(ans[1 .. $]); } failed: } } catch (EOFException e) { } }