P14257 Jealousy

Little S is going to interview at the bookstore where Little Y works part-time, but she wants to keep it a secret for now. There are a total of $n$ interviews. The first interview starts when the bookstore opens, and each interview lasts for $s$ minutes, with the next one immediately following the previous one. Specifically, let the bookstore opening time be minute $0$. The $i$-th interview takes place from minute $(i-1)\times s$ to minute $i\times s$. Little Y arrives at the bookstore to work at minute $y$. He starts from the interview room door, inspects around the bookshelves, and returns to the interview room door every $t$ minutes. Specifically, he will be at the interview room door at minute $y+j\times t$, where $j$ is a non-negative integer. If Little Y is exactly at the interview room door when Little S's interview starts or ends, she will be discovered. Little S wants to know whether there exists at least one interview among the $n$ interviews that she can attend without being discovered. In other words, whether there exists a positive integer $i$ satisfying $1\le i\le n$, and there is no non-negative integer $j$ such that $(i-1)\times s=y+j\times t$ or $i\times s=y+j\times t$.

Input a single line containing four integers $n, y, s, t$, representing the number of interviews, the start time of Little Y's work, the duration of one interview, and the time it takes to complete one round of inspection, respectively.

Output a string on a single line: if there is an interview that Little S can attend without being discovered, output `Yes`; otherwise, output `No`.

**【Sample 1 Explanation】** Little Y is at the interview room door at minutes $0, 5, 10, \dots$. The first interview lasts from minute $0$ to minute $2$, and would be discovered at minute $0$; the second interview lasts from minute $2$ to minute $4$. If Little S attends this one, she will not be discovered, so output `Yes`. **【Sample 2 Explanation】** Little Y is at the interview room door at minutes $0, 9, 18, \dots$. The only interview Little S can attend lasts from minute $0$ to minute $1$, and would be discovered at minute $0$, so output `No`. **【Sample 3】** See jealousy3.in and jealousy3.ans in the problem attachment. This sample satisfies special properties AB. **【Sample 4】** See jealousy4.in and jealousy4.ans in the problem attachment. This sample satisfies special properties BC. **【Data Range】** For all test data, it is guaranteed that: $1 \le n \le 10$, $0 \le y \le 30$, $1 \le s, t \le 30$. ::cute-table{tuack} | Test Data ID | $n \le$ | Special Properties | | :-: | :-: | :-: | | $1$ | $1$ | A | | $2\sim3$ | $10$ | B | | $4$ | ^ | AB | | $5\sim6$ | ^ | C | | $7\sim10$ | ^ | None | Special Property A: It is guaranteed that $y = 0$. Special Property B: It is guaranteed that $t \mid (2 \times s)$. Special Property C: It is guaranteed that $s < y$. Here, $a \mid b$ denotes that $a$ divides $b$, meaning there exists an integer $c$ such that $a \times c = b$.