Practice

문제

John practiced for $NN$ days in preparation for the olympiad. He solved $X_{i}X\_i$ tasks on day $ii$.

After the olympiad he wanted to know whether there was a span of consecutive days when he solved exacly $YY$ tasks. In other words, are there integers $aa$ and $bb$ such that $1\le a\le b\le N1\; \backslash le\; a\; \backslash le\; b\; \backslash le\; N$ and $X_a+X_{a+1}+\dots +X_b=YX\_a\; +\; X\_\{a+1\}\; +\; \backslash ldots\; +\; X\_b\; =\; Y$?

Write a program to help John answer that question.

입력

The first line of input contains $NN$, the number of days ($1\le N\le 10001\; \backslash le\; N\; \backslash le\; 1\backslash ,000$), and $MM$, the number of questions ($1\le M\le 10000001\; \backslash le\; M\; \backslash le\; 1\backslash ,000\backslash ,000$).

The second line contains $NN$ space-separated integers $X_{i}X\_i$ ($0\le X_i\le 10000\; \backslash le\; X\_i\; \backslash le\; 1\backslash ,000$, where $1\le i\le N1\; \backslash le\; i\; \backslash le\; N$), the numbers of tasks John solved each day.

The third line contains $MM$ space-separated integers $Y_{j}Y\_j$ ($1\le Y_j\le 10000001\; \backslash le\; Y\_j\; \backslash le\; 1\backslash ,000\backslash ,000$, where $1\le j\le M1\; \backslash le\; j\; \backslash le\; M$), the numbers of tasks in John's questions.

출력

Output $MM$ lines, one per question. On the line $jj$ output the word 'JAH', if there exists a span of consecutive days when John solved exactly $Y_{j}Y\_j$ tasks, or the word 'EI', if there's no such span of days.

3 4
1 2 3
2 7 5 4

JAH
EI
JAH
EI