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();
      }
      
      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;
        }
      }
      
      if (A[0] == 1) {
        foreach (x; 1 .. prod - 1) {
          write(0);
        }
        foreach (x; prod - 1 .. X + 1) {
          write(1);
        }
        goto failed;
      }
      
      {
        const lb = cast(int)(prod - 1);
        const m = X - lb + 1;
        auto ans = new bool[m];
        debug {
          writeln("lb = ", lb, ", m = ", m);
        }
        
        void solve(int l, int r, bool[] dp) {
          if (l + 1 == r) {
            debug {
              writeln(l, ": ", dp);
            }
            foreach (x; 0 .. m) {
              ans[x] = ans[x] || dp[x];
            }
            return;
          }
          const mid = (l + r) / 2;
          auto DP = new bool[m];
          DP[] = dp[];
          foreach (i; mid .. r) {
            foreach (x; A[i] .. m) {
              if (DP[x - A[i]]) {
                DP[x] = true;
              }
            }
          }
          solve(l, mid, DP);
          DP[] = dp[];
          foreach (i; l .. mid) {
            foreach (x; A[i] .. m) {
              if (DP[x - A[i]]) {
                DP[x] = true;
              }
            }
          }
          solve(mid, r, DP);
        }
        
        auto dp = new bool[m];
        dp[0] = true;
        solve(0, N, dp);
        
        foreach (x; 1 .. lb) {
          write(0);
        }
        foreach (x; 0 .. m) {
          write(ans[x] ? 1 : 0);
        }
        writeln();
      }
     failed:
    }
  } catch (EOFException e) {
  }
}