Once upon a time in the small town of Pairland, there was an annual lottery event that captivated the residents. The lottery involved N magical coins, each represented by two values (Ai, Bi), one on each side. The townsfolk eagerly awaited the grand lottery day, and the excitement was palpable. However, a mysterious condition was imposed on the lottery this year. Each participant had to swap the sides of some coin pairs, following a special operation: for the ith pair, Ai would become Bi , and Bi would become Ai. To add a twist to the event, the townspeople were given an intriguing challenge. They had to figure out if it was possible to perform these swaps in such a way that the sum of all the values on one side of the coins equaled a magical number, M. Your task is to create a question for participants in the magical lottery of Pairland. They must decide if it's possible to swap coin values in such a way that the sum of one side equals a magical number, M. If possible, print "YES"; otherwise, print "NO."Input FormatThe first line contains an integer T denoting the number of test cases. Description of each test case is as follows: The first line of each test case contains two space-seperated integers N and M denoting Number of Coins and the Magical Number respectively. The next N lines contains two space-seperated integers Ai and Bi denoting the ith pair.Constraints1 <= T <= 1001 <= N <= 10001 <= M <= 100001 <= Ai, Bi <= 1000Output FormatFor each test case, print YES, if it is possible to satisfy the given condition, otherwise print NO.Sample Input 032 54 105 12 32 14 34 193 71 46 93 6Sample Output 0YESNOYESExplanation 0For Testcase 1:You choose side containing 4 for coin 1 and side containing 1 for coin 2. Hence the answer is YES.For Testcase 2:You cannot get 3 by choosing any combination of sides, hence the answer is NO

"The morning of June 27th was clear and sunny, with the fresh warmth of a full-summer day; the flowers were blossoming profusely and the grass was richly green. The people of the village began to gather in the square, between the post office and the bank, around ten o'clock; in some towns there were so many people that the lottery took two days and had to be started on June 26th, but in this village, where there were only about three hundred people, the whole lottery took less than two hours, so it could begin at ten o'clock in the morning and still be through in time to allow the villagers to get home for noon dinner." -The Lottery by Shirley Jackson Which element of a narrative is BEST exemplified by this excerpt?Group of answer choicesSettingThemeChractersPlot

The people of the village began to gather in the square, between the post office and the bank, around ten o'clock; in some towns there were so many people that the lottery took two days and had to be started on June 25th. But in this village, where there were only about three hundred people, the whole lottery took less than two hours, so it could begin at ten o'clock in the morning and still be through in time to allow the villagers to get home for noon dinner.— Shirley Jackson, "The Lottery," 194807:06Three days later, the Dursleys were showing no sign of relenting, and Harry couldn't see any way out of his situation. He lay on his bed watching the sun sinking behind the bars on the window and wondered miserably what was going to happen to him.What was the good of magicking himself out of his room if Hogwarts would expel him for doing it? Yet life at Privet Drive had reached an all-time low. Now that the Dursleys knew they weren't going to wake up as fruit bats, he had lost his only weapon. Dobby might have saved Harry from horrible happenings at Hogwarts, but the way things were going, he'd probably starve to death anyway.— J. K. Rowling, Harry Potter, and the Chamber of Secrets, 199907:06Christmas won't be Christmas without any presents," grumbled Jo, lying on the rug."It's so dreadful to be poor!" sighed Meg, looking down at her old dress."I don't think it's fair for some girls to have plenty of pretty things, and other girls nothing at all," added little Amy, with an injured sniff."We've got Father and Mother, and each other," said Beth contentedly from her corner.The four young faces on which the firelight shone brightened at the cheerful words, but darkened again as Jo said sadly, "We haven't got Father, and shall not have him for a long time." She didn't say "perhaps never," but each silently added it, thinking of Father far away, where the fighting was.— Louisa May Alcott, Little Women, 186807:06At the subway station, you wait fifteen minutes on the platform for a train. Finally, a local, enervated by graffiti, shuffles into the station. You get a seat and hoist a copy of the New York Post. The post is the most shameful of your several addictions.— Jay McInerney, Bright Lights, Big City, 198407:06There was no possibility of taking a walk that day. We had been wandering, indeed, in the leafless shrubbery an hour in the morning; but since dinner (Mrs. Reed, when there was no company, dined early) the cold winter wind had brought with it clouds so sombre, and a rain so penetrating, that further outdoor exercise was now out of the question.I was glad of it: I never liked long walks, especially on chilly afternoons: dreadful to me was the coming home in the raw twilight, with nipped fingers and toes, and a heart saddened by the chidings of Bessie, the nurse, and humbled by the consciousness of my physical inferiority to Eliza, John, and Georgiana Reed.— Charlotte Brontë, Jane Eyre, 1847

Alice, Bob, and Confucius are bored during recess, so they decide to play a new game. Each of them puts a dollar in the pot, and each tosses a coin. Alice wins if the coins land all heads or all tails. Bob wins if two heads and one tail land, and Confucius wins if one head and two tails land. The coins are fair, and the winner receives a net payment of $2 ($3 - $1 = $2), and the losers lose their $1.

The King wants to marry off his daughter, and he wants her husband to have the greatest innate luckiness possible. To find such a person he decided to hold a heads-or-tails tournament.If person A𝐴 with luckiness x𝑥 and person B𝐵 with luckiness y𝑦 play heads-or-tails against each other, person A𝐴 wins with probability x/(x+y)𝑥/(𝑥+𝑦).The tournament has several rounds. Each round some participants are split into pairs. Each pair plays against each other, and the loser leaves the tournament.The participants are numbered from 11 to n𝑛. During the first round, a number k𝑘 (1≤k≤n1≤𝑘≤𝑛) is selected such that n−k/2𝑛−𝑘/2 is a power of 22 (such k𝑘 always exists and is unique). Only participants numbered from 11 to k𝑘 take part in the first round. It ensures that in all other rounds the number of participants is the power of 22.During other rounds, all the participants who still have not left the tournament take part. If during some round, participants numbered p1<…<p2m𝑝1<…<𝑝2𝑚 take part, then they are split into pairs in the following manner: participant p2i−1𝑝2𝑖−1 plays against participant p2i𝑝2𝑖 for each i𝑖 from 11 to m𝑚.The rounds are held until only one participant is left. He is declared the winner of the tournament and he will marry the King's daughter. The princess can't wait to find out who is her future husband. She asked every participant to tell her his luckiness. Assuming they did not lie, she wants to know the probability of each participant winning the tournament. As you are the best friend of the princess, she asks you to help her.InputThe first line of the input contains the number of participants, n𝑛 (2≤n≤3⋅1052≤𝑛≤3⋅105). The second line of the input contains n𝑛 integer numbers, a1,…,an𝑎1,…,𝑎𝑛 (1≤ai≤1091≤𝑎𝑖≤109). The luckiness of the i𝑖-th participant equals to ai𝑎𝑖.OutputPrint n𝑛 numbers pi𝑝𝑖. The i𝑖-th number should be the probability of the i𝑖-th participant winning the tournament. The absolute error of your answer must not exceed 10−910−9.ExampleinputCopy51 4 1 1 4outputCopy0.026 0.3584 0.0676 0.0616 0.4864NoteHere is an example of a tournament bracket, showing the winning probability in each pair.

Yet Another Coin Problem