{"problem":{"name":"Construct Highway","description":{"content":"The Republic of Atcoder has $N$ towns numbered $1$ through $N$, and $M$ highways numbered $1$ through $M$.   Highway $i$ connects Town $A_i$ and Town $B_i$ bidirectionally. King Takahashi is going to ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc239_f"},"statements":[{"statement_type":"Markdown","content":"The Republic of Atcoder has $N$ towns numbered $1$ through $N$, and $M$ highways numbered $1$ through $M$.  \nHighway $i$ connects Town $A_i$ and Town $B_i$ bidirectionally.\nKing Takahashi is going to construct $(N-M-1)$ new highways so that the following two conditions are satisfied:\n\n*   One can travel between every pair of towns using some number of highways\n*   For each $i=1,\\ldots,N$, exactly $D_i$ highways are directly connected to Town $i$\n\nDetermine if there is such a way of construction. If it exists, print one.\n\n## Constraints\n\n*   $2 \\leq N \\leq 2\\times 10^5$\n*   $0 \\leq M \\lt N-1$\n*   $1 \\leq D_i \\leq N-1$\n*   $1\\leq A_i \\lt B_i \\leq N$\n*   If $i\\neq j$, then $(A_i, B_i) \\neq (A_j,B_j)$.\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$\n$D_1$ $\\ldots$ $D_N$\n$A_1$ $B_1$\n$\\vdots$\n$A_M$ $B_M$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc239_f","tags":[],"sample_group":[["6 2\n1 2 1 2 2 2\n2 3\n1 4","6 2\n5 6\n4 5\n\nAs in the Sample Output, the conditions can be satisfied by constructing highways connecting Towns $6$ and $2$, Towns $5$ and $6$, and Towns $4$ and $5$, respectively.\nAnother example to satisfy the conditions is to construct highways connecting Towns $6$ and $4$, Towns $5$ and $6$, and Towns $2$ and $5$, respectively."],["5 1\n1 1 1 1 4\n2 3","\\-1"],["4 0\n3 3 3 3","\\-1"]],"created_at":"2026-03-03 11:01:13"}}