# [Usaco2010 Dec]The Trough Game

时间限制：10s 空间限制：64MB

### 题目描述

Farmer John and Bessie are playing games again. This one has to do with troughs of water. Farmer John has hidden N (1 <= N <= 20) troughs behind the barn, and has filled some of them with food. Bessie has asked M (1 <= M <= 100) questions of the form, "How many troughs from this list (which she recites) are filled?". Bessie needs your help to deduce which troughs are actually filled. Consider an example with four troughs where Bessie has asked these questions (and received the indicated answers): 1) "How many of these troughs are filled: trough 1" --> 1 trough is filled 2) "How many of these troughs are filled: troughs 2 and 3" --> 1 trough is filled 3) "How many of these troughs are filled: troughs 1 and 4" --> 1 trough is filled 4) "How many of these troughs are filled: troughs 3 and 4" --> 1 trough is filled From question 1, we know trough 1 is filled. From question 3, we then know trough 4 is empty. From question 4, we then know that trough 3 is filled. From question 2, we then know that trough 2 is empty. 求N位二进制数X，使得给定的M个数，满足X and Bi=Ci ,Bi ci分别是读入的两个数

### 输入格式

* Line 1: Two space-separated integers: N and M * Lines 2..M+1: A subset of troughs, specified as a sequence of contiguous N 0's and 1's, followed by a single integer that is the number of troughs in the specified subset that are filled.

### 输出格式

* Line 1: A single line with: * The string "IMPOSSIBLE" if there is no possible set of filled troughs compatible with Farmer John's answers. * The string "NOT UNIQUE" if Bessie cannot determine from the given data exactly what troughs are filled. * Otherwise, a sequence of contiguous N 0's and 1's specifying which troughs are filled.

### 样例输入

4 4 1000 1 0110 1 1001 1 0011 1

### 样例输出

1010

### 提示

没有写明提示

### 题目来源

Silver