{"problem":{"name":"095. Techno Pop","description":{"content":"Techno Pop After listening to the Kraftwerk song Techno Pop, you decide that you want to pop a balloon. You have a spherical balloon that will pop when it reaches a volume of $v 1$ in^3, and you blow","description_type":"Markdown"},"platform":"Codeforces","limit":{"time_limit":1000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"CF10269095"},"statements":[{"statement_type":"Markdown","content":"Techno Pop\n\nAfter listening to the Kraftwerk song Techno Pop, you decide that you want to pop a balloon. You have a spherical balloon that will pop when it reaches a volume of $v 1$ in^3, and you blow up the balloon inside of a cube-shaped box with a volume of $v 2$ in^3.\n\nGiven these values, figure out whether or not it is possible to pop the balloon in the cube-shaped box that you have.\n\nRecall that the formula for the volume of a sphere is $frac(4, 3) pi r^3$, where $r$ represents the radius of the sphere, and the formula for the volume of a cube (or a cube-shaped box) is $s^3$, where $s$ represents the side length of the cube.\n\nThe only line of input contains two space-separated integers: $v 1$ and $v 2$, representing the volume that the spherical balloon needs to be greater than or equal to in order to pop, and the volume of the cube-shaped box, respectively. Both values are given in $i n^3$.\n\nOutput \"YES\" (no quotes) if the balloon can pop inside of the box, and \"NO\" (no quotes) otherwise.\n\nIn the first example case, the balloon has room to inflate to at most 14.1 $i n^3$, so the balloon can inflate to 10 $i n^3$ and pop.\n\nIn the second example case, the balloon only has room to inflate to 4.2 $i n^3$, so the balloon cannot pop inside of the cube-shaped box.\n\n## Input\n\nThe only line of input contains two space-separated integers: $v 1$ and $v 2$, representing the volume that the spherical balloon needs to be greater than or equal to in order to pop, and the volume of the cube-shaped box, respectively. Both values are given in $i n^3$.\n\n## Output\n\nOutput \"YES\" (no quotes) if the balloon can pop inside of the box, and \"NO\" (no quotes) otherwise.\n\n[samples]\n\n## Note\n\nIn the first example case, the balloon has room to inflate to at most 14.1 $i n^3$, so the balloon can inflate to 10 $i n^3$ and pop.In the second example case, the balloon only has room to inflate to 4.2 $i n^3$, so the balloon cannot pop inside of the cube-shaped box.","is_translate":false,"language":"English"},{"statement_type":"Markdown","content":"**Definitions**  \nLet $ v_1 \\in \\mathbb{R}^+ $ be the minimum volume required for the balloon to pop.  \nLet $ v_2 \\in \\mathbb{R}^+ $ be the volume of the cube-shaped box.  \n\n**Constraints**  \nThe balloon is spherical and must fit entirely within the cube.  \nThe maximum radius $ r_{\\text{max}} $ of the balloon is constrained by the cube’s side length $ s = \\sqrt[3]{v_2} $:  \n$$\nr_{\\text{max}} = \\frac{s}{2} = \\frac{\\sqrt[3]{v_2}}{2}\n$$  \n\n**Objective**  \nCompute the maximum possible volume $ V_{\\text{max}} $ of the balloon inside the cube:  \n$$\nV_{\\text{max}} = \\frac{4}{3} \\pi r_{\\text{max}}^3 = \\frac{4}{3} \\pi \\left( \\frac{\\sqrt[3]{v_2}}{2} \\right)^3 = \\frac{\\pi}{6} v_2\n$$  \n\nDetermine whether:  \n$$\nV_{\\text{max}} \\geq v_1\n$$  \n\nOutput \"YES\" if $ \\frac{\\pi}{6} v_2 \\geq v_1 $, otherwise \"NO\".","is_translate":false,"language":"Formal"}],"meta":{"iden":"CF10269095","tags":[],"sample_group":[],"created_at":"2026-03-03 11:00:39"}}