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문제

What an unsmurfy day!  Smurfette just found out that someone (probably Jokey Smurf) has stolen all of her clothes and she'll need to buy new ones.  There are $n$ sets of clothes in the shop each having different integer price from $1$ to $n$ smurfcoins. Since smurfiness of an article of clothing is proportional to its price Smurfette wants to spend all of her $s$ smurfcoins.  However her wardrobe will fit only $k$ clothes so she needs to buy exactly $k$ (having empty places in a wardrobe is bad for her image).

입력

First line of input file contains the number of testcases $t$ ($t \leq 8000$). Each testcase consists of a single line containing three integers $n$, $s$, and $k$ ($1 \leq k \leq n \leq 40\,000$, $0 \leq s \leq 10^9$). $n$ is the number of clothes available in the shop, $k$ is the number of clothes Smurfette wants to buy, and $s$ is the amount of smurfcoins she wants to spend.

출력

For each testcase output on a single line the word "YES" (without quotes) if it is possible to buy $k$ clothes so that their price is $s$, or "NO" otherwise.  If the answer is "YES" then on the following line output a string of $n$ digits $a_i$.  $a_i$ should be $1$ if Smurfette should buy article of clothing with price $i$, otherwise $a_i$ should be $0$.

예제 입력 1

3
3 6 2
5 7 3
1 1 1

예제 출력 1

NO
YES
11010
YES
1