{"raw_statement":[{"iden":"statement","content":"Kirill plays a new computer game. He came to the potion store where he can buy any potion. Each potion is characterized by two integers — amount of experience and cost. The efficiency of a potion is the ratio of the amount of experience to the cost. Efficiency may be a non-integer number.\n\nFor each two integer numbers _a_ and _b_ such that _l_ ≤ _a_ ≤ _r_ and _x_ ≤ _b_ ≤ _y_ there is a potion with experience _a_ and cost _b_ in the store (that is, there are (_r_ - _l_ + 1)·(_y_ - _x_ + 1) potions).\n\nKirill wants to buy a potion which has efficiency _k_. Will he be able to do this?"},{"iden":"input","content":"First string contains five integer numbers _l_, _r_, _x_, _y_, _k_ (1 ≤ _l_ ≤ _r_ ≤ 107, 1 ≤ _x_ ≤ _y_ ≤ 107, 1 ≤ _k_ ≤ 107)."},{"iden":"output","content":"Print \"_YES_\" without quotes if a potion with efficiency exactly _k_ can be bought in the store and \"_NO_\" without quotes otherwise.\n\nYou can output each of the letters in any register."},{"iden":"examples","content":"Input\n\n1 10 1 10 1\n\nOutput\n\nYES\n\nInput\n\n1 5 6 10 1\n\nOutput\n\nNO"}],"translated_statement":[{"iden":"statement","content":"Kirill 正在玩一款新电脑游戏。他来到一家药水商店，可以购买任意药水。每种药水由两个整数表征——经验值和价格。药水的效率是经验值与价格的比值，效率可能不是整数。\n\n对于每一对整数 #cf_span[a] 和 #cf_span[b]，满足 #cf_span[l ≤ a ≤ r] 且 #cf_span[x ≤ b ≤ y]，商店中都存在一种经验值为 #cf_span[a]、价格为 #cf_span[b] 的药水（即共有 #cf_span[(r - l + 1)·(y - x + 1)] 种药水）。\n\nKirill 希望购买一种效率恰好为 #cf_span[k] 的药水。他能办到吗？\n\n第一行包含五个整数 #cf_span[l], #cf_span[r], #cf_span[x], #cf_span[y], #cf_span[k]（#cf_span[1 ≤ l ≤ r ≤ 10^7], #cf_span[1 ≤ x ≤ y ≤ 10^7], #cf_span[1 ≤ k ≤ 10^7]）。\n\n如果商店中存在一种效率恰好为 #cf_span[k] 的药水，则输出 \"_YES_\"（不含引号）；否则输出 \"_NO_\"（不含引号）。\n\n你可以以任意大小写输出字母。"},{"iden":"input","content":"第一行包含五个整数 #cf_span[l], #cf_span[r], #cf_span[x], #cf_span[y], #cf_span[k]（#cf_span[1 ≤ l ≤ r ≤ 10^7], #cf_span[1 ≤ x ≤ y ≤ 10^7], #cf_span[1 ≤ k ≤ 10^7]）。"},{"iden":"output","content":"如果商店中存在一种效率恰好为 #cf_span[k] 的药水，则输出 \"_YES_\"（不含引号）；否则输出 \"_NO_\"（不含引号）。你可以以任意大小写输出字母。"},{"iden":"examples","content":"输入\n1 10 1 10 1\n输出\nYES\n\n输入\n1 5 6 10 1\n输出\nNO"}],"sample_group":[],"show_order":[],"formal_statement":"**Definitions**  \nLet $ l, r, x, y, k \\in \\mathbb{Z}^+ $ with $ 1 \\leq l \\leq r \\leq 10^7 $, $ 1 \\leq x \\leq y \\leq 10^7 $, $ 1 \\leq k \\leq 10^7 $.  \n\nThe set of possible potions is:  \n$$\nP = \\{ (a, b) \\in \\mathbb{Z}^2 \\mid a \\in [l, r],\\ b \\in [x, y] \\}\n$$  \nThe efficiency of a potion $ (a, b) \\in P $ is $ \\frac{a}{b} $.  \n\n**Objective**  \nDetermine whether there exists a pair $ (a, b) \\in P $ such that:  \n$$\n\\frac{a}{b} = k\n$$  \n\nEquivalently, determine whether there exist integers $ a \\in [l, r] $, $ b \\in [x, y] $ such that:  \n$$\na = k \\cdot b\n$$","simple_statement":null,"has_page_source":false}