{"problem":{"name":"Product Simulation","description":{"content":"This is an output-only problem. You shouldn't read anything from the input. In short, your task is to simulate multiplication by using only comparison $(x < y)$ and addition $(x + y)$. There is no inp","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc047_e"},"statements":[{"statement_type":"Markdown","content":"This is an output-only problem. You shouldn't read anything from the input.\nIn short, your task is to simulate multiplication by using only comparison $(x < y)$ and addition $(x + y)$. There is no input in this problem, you just print a sequence of operations.\nImagine that there is a big array $a[0], a[1], ..., a[N-1]$ of length $N$. The first two values are initially two non-negative integers $A$ and $B$ (which are unknown to you), the other elements are zeros. Your goal is to get the product $A \\cdot B$ in $a[2]$ at the end.\nYou are allowed operations of two types, with the following format (where $0 \\leq i, j, k < N$):\n\n*   `+ i j k` — applies operation $a[k] = a[i] + a[j]$.\n*   `< i j k` — applies operation $a[k] = a[i] < a[j]$. That is, if $a[i] < a[j]$ then $a[k]$ becomes $1$, otherwise it becomes $0$.\n\nYou can use at most $Q$ operations. Elements of $a$ can't exceed $V$. Indices $(i, j, k)$ don't have to be distinct. It's allowed to modify any element of the array (including the first two). The actual checker simulates the process for multiple pairs $(A, B)$ within a single test. Each time, the checker chooses values $A$ and $B$, creates the array $a = [A, B, 0, 0, \\ldots, 0]$, applies all your operations and ensures that $a[2] = A \\cdot B$.\n\n## Constraints\n\n*   $0 \\leq A, B \\leq 10^9$\n*   $N = Q = 200\\,000$\n*   $V = 10^{19} = 10\\,000\\,000\\,000\\,000\\,000\\,000$\n\n## Input\n\nThe Standard Input is empty.\n\n## Partial Score\n\n*   $800$ points will be awarded for passing tests that satisfy $A, B \\leq 10$.\n*   Another $1000$ points will be awarded for passing all tests.\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc047_e","tags":[],"sample_group":[],"created_at":"2026-03-03 11:01:14"}}