B"There are n officers in the Army of Byteland. Each officer has some power associated with him. The power of the i -th officer is denoted by p_{i} . As the war is fast approaching, the General would like to know the strength of the army. The strength of an army is calculated in a strange way in Byteland. The General selects a random subset of officers from these n officers and calls this subset a battalion.(All 2^n subsets of the n officers can be chosen equally likely, including empty subset and the subset of all officers). The strength of a battalion is calculated in the following way: Let the powers of the chosen officers be a_{1},a_{2}, ldots,a_{k} , where a_1 <= a_2 <= ... <= a_k . The strength of this battalion is equal to a_1a_2 + a_2a_3 + ... + a_{k-1}a_k . (If the size of Battalion is <= q 1 , then the strength of this battalion is 0 ). The strength of the army is equal to the expected value of the strength of the battalion. As the war is really long, the powers of officers may change. Precisely, there will be q changes. Each one of the form i x indicating that p_{i} is changed to x . You need to find the strength of the army initially and after each of these q updates. Note that the changes are permanent. The strength should be found by modulo 10^{9}+7 . Formally, let M=10^{9}+7 . It can be shown that the answer can be expressed as an irreducible fraction p/q , where p and q are integers and q not equiv 0 bmod M ). Output the integer equal to p cdot q^{-1} bmod M . In other words, output such an integer x that 0 <= q x < M and x xe2 x8b x85 q equiv p bmod M ). The first line of the input contains a single integer n ( 1 <= q n <= q 3 xe2 x8b x8510^{5} ) -- the number of officers in Byteland's Army. The second line contains n integers p_{1},p_{2}, ldots,p_{n} ( 1 <= q p_{i} <= q 10^{"...