{"problem":{"name":"Not Equal","description":{"content":"You are given a sequence $C$ of $N$ integers. Find the number of sequences $A$ of $N$ integers satisfying all of the following conditions. *   $1 \\leq A_i \\leq C_i\\, (1 \\leq i \\leq N)$ *   $A_i \\neq ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc209_c"},"statements":[{"statement_type":"Markdown","content":"You are given a sequence $C$ of $N$ integers. Find the number of sequences $A$ of $N$ integers satisfying all of the following conditions.\n\n*   $1 \\leq A_i \\leq C_i\\, (1 \\leq i \\leq N)$\n*   $A_i \\neq A_j\\, (1 \\leq i < j \\leq N)$\n\nSince the count may be enormous, print it modulo $(10^9+7)$.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq C_i \\leq 10^9$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$C_1$ $C_2$ $\\ldots$ $C_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc209_c","tags":[],"sample_group":[["2\n1 3","2\n\nWe have two sequences $A$ satisfying all of the conditions: $(1,2)$ and $(1,3)$.  \nOn the other hand, $A=(1,1)$, for example, does not satisfy the second condition."],["4\n3 3 4 4","12"],["2\n1 1","0\n\nWe have no sequences $A$ satisfying all of the conditions, so we should print $0$."],["10\n999999917 999999914 999999923 999999985 999999907 999999965 999999914 999999908 999999951 999999979","405924645\n\nBe sure to print the count modulo $(10^9+7)$."]],"created_at":"2026-03-03 11:01:14"}}