Uninitialized Local Array

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

A local integer array $a$ with $n$ elements is created without an initializer. Initially, no element is considered to contain a defined value that the program may use.

Then $m$ assignments are performed. Each assignment gives an index $i$ and a value $x$, meaning $a_i=x$. An element assigned at least once becomes defined; if the same index is assigned multiple times, the latest value is kept.

Finally, $q$ element reads are requested. For each requested index, print its current value if it has been assigned. If it has never been assigned, do not read or guess its value; print INDETERMINATE instead.

Input

• The first line contains $n$ and $m$.
• Each of the next $m$ lines contains $i$ and $x$, representing the assignment $a_i=x$.
• The next line contains $q$.
• The final line contains exactly $q$ indices to inspect.

Every input index lies in $[0,n-1]$.

Output

For each requested index, print one line containing either its current assigned value or INDETERMINATE if it has never been assigned.

Subtasks

Subtask 1 (100 points): $1\le n\le1000$, $0\le m\le1000$, $1\le q\le1000$, $-10^9\le x\le10^9$.

Examples

Input

6 3
0 7
2 -4
5 9
6
0 1 2 3 4 5

Output

7
INDETERMINATE
-4
INDETERMINATE
INDETERMINATE
9

Explanation

The array has $6$ elements. The assignments define $a_0=7$, $a_2=-4$, and $a_5=9$.

The queries inspect indices $0,1,2,3,4,5$. Only indices $0,2,5$ have been assigned, so the other positions must be reported as INDETERMINATE instead of reading an uninitialized value.