For an array (a) of length (n) and three integers (x), (l), and (r)（(1 \le l \le r \le n)), define: () f(a,x,l,r) = \begin{cases} 0, & \text{if} & (x-\min_{j=l}^{r}(a_j)) \cdot (x-\max_{j=l}^{r}(a_j))) < 0 \\ 1, & \text{if} & (x-\min_{j=l}^{r}(a_j)) \cdot (x-\max_{j=l}^{r}(a_j))) \ge 0 \end{cases} () You are given an array (a) of length (n) ((1 \le a_i \le n)), and (m) intervals (l_i, r_i) ((1 \le l_i \le r_i \le n)). For each (x=1, 2, \dots, n), answer the following question independently : Does there exist a rearrangement (a') of (a), such that for all (1 \le i \le m), (f(a',x,l_i,r_i) = 1)? The first line contains a single integer (t) ((1 \le t \le 2 \cdot 10^4)) — the number of test cases. Description of each testcase follows. The first line contains two integers (n) and (m) ((2 \le n \le 2000), (1 \le m \le 2000)). The next line contains (n) space-separated integers (a_1, a_2, \cdots, a_n) ((1 \le a_i \le n)). The next (m) lines each contain two space-separated integers (l_i, r_i) ((1 \le l_i \le r_i \le n)), each denoting an interval. It is guaranteed that the sum of (n^2) and the sum of (m^2) over all test cases does not exceed (4 \cdot 10^6), respectively. For each test case, output a binary string (s). For (x=1,2,\ldots,n), (s_x=1) only if there exists a rearrangement (a') of (a), such that for all (1 \le i \le m), (f(a',x,l_i,r_i) = 1). Otherwise, (s_x=0). In the first test case, For (x=1), one valid rearrangement is (a'=1,1,3,4). For (x=2), there is no rearrangement (a') of (a) satisfying (f(a',2,1,2)=f(a',2,2,4)=1). For (x=3), the only valid rearrangement is (a'=4,3,1,1). For (x=4), one valid rearrangement is (a'=1,1,3,4).