{"problem":{"name":"Sum of Large Numbers","description":{"content":"We have $N+1$ integers: $10^{100}$, $10^{100}+1$, ..., $10^{100}+N$. We will choose $K$ or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo $(10^9+7)","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc163_d"},"statements":[{"statement_type":"Markdown","content":"We have $N+1$ integers: $10^{100}$, $10^{100}+1$, ..., $10^{100}+N$.\nWe will choose $K$ or more of these integers. Find the number of possible values of the sum of the chosen numbers, modulo $(10^9+7)$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2\\times 10^5$\n*   $1 \\leq K \\leq N+1$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc163_d","tags":[],"sample_group":[["3 2","10\n\nThe sum can take $10$ values, as follows:\n\n*   $(10^{100})+(10^{100}+1)=2\\times 10^{100}+1$\n*   $(10^{100})+(10^{100}+2)=2\\times 10^{100}+2$\n*   $(10^{100})+(10^{100}+3)=(10^{100}+1)+(10^{100}+2)=2\\times 10^{100}+3$\n*   $(10^{100}+1)+(10^{100}+3)=2\\times 10^{100}+4$\n*   $(10^{100}+2)+(10^{100}+3)=2\\times 10^{100}+5$\n*   $(10^{100})+(10^{100}+1)+(10^{100}+2)=3\\times 10^{100}+3$\n*   $(10^{100})+(10^{100}+1)+(10^{100}+3)=3\\times 10^{100}+4$\n*   $(10^{100})+(10^{100}+2)+(10^{100}+3)=3\\times 10^{100}+5$\n*   $(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=3\\times 10^{100}+6$\n*   $(10^{100})+(10^{100}+1)+(10^{100}+2)+(10^{100}+3)=4\\times 10^{100}+6$"],["200000 200001","1\n\nWe must choose all of the integers, so the sum can take just $1$ value."],["141421 35623","220280457"]],"created_at":"2026-03-03 11:01:13"}}