{"problem":{"name":"Change a Little Bit","description":{"content":"For two sequences $S$ and $T$ of length $N$ consisting of $0$ and $1$, let us define $f(S, T)$ as follows: *   Consider repeating the following operation on $S$ so that $S$ will be equal to $T$. $f(S","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc150_e"},"statements":[{"statement_type":"Markdown","content":"For two sequences $S$ and $T$ of length $N$ consisting of $0$ and $1$, let us define $f(S, T)$ as follows:\n\n*   Consider repeating the following operation on $S$ so that $S$ will be equal to $T$. $f(S, T)$ is the minimum possible total cost of those operations.\n    *   Change $S_i$ (from $0$ to $1$ or vice versa). The cost of this operation is $D \\times C_i$, where $D$ is the number of integers $j$ such that $S_j \\neq T_j (1 \\leq j \\leq N)$ just before this change.\n\nThere are $2^N \\times (2^N - 1)$ pairs $(S, T)$ of different sequences of length $N$ consisting of $0$ and $1$. Compute the sum of $f(S, T)$ over all of those pairs, 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$C_1$ $C_2$ $\\cdots$ $C_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc150_e","tags":[],"sample_group":[["1\n1000000000","999999993\n\nThere are two pairs $(S, T)$ of different sequences of length $2$ consisting of $0$ and $1$, as follows:\n\n*   $S = (0), T = (1):$ by changing $S_1$ to $1$, we can have $S = T$ at the cost of $1000000000$, so $f(S, T) = 1000000000$.\n*   $S = (1), T = (0):$ by changing $S_1$ to $0$, we can have $S = T$ at the cost of $1000000000$, so $f(S, T) = 1000000000$.\n\nThe sum of these is $2000000000$, and we should print it modulo $(10^9+7)$, that is, $999999993$."],["2\n5 8","124\n\nThere are $12$ pairs $(S, T)$ of different sequences of length $3$ consisting of $0$ and $1$, which include:\n\n*   $S = (0, 1), T = (1, 0)$\n\nIn this case, if we first change $S_1$ to $1$ then change $S_2$ to $0$, the total cost is $5 \\times 2 + 8 = 18$. We cannot have $S = T$ at a smaller cost, so $f(S, T) = 18$."],["5\n52 67 72 25 79","269312"]],"created_at":"2026-03-03 11:01:14"}}