In ICPCCamp, there are n switches and m bulbs.The m bulbs are ON at the beginning.Bobo knows in advance an n x m binary matrix Ci, j. When the i-th switch is pressed, all the bulbs j satisfying Ci, j = 1 flip its state between ON and OFF.Let f be the number of bulbs staying ON after the switches in set S is pressed. Find the sum of f3 modulo over all 2n possible choices of S.
In ICPCCamp, there are n switches and m bulbs.The m bulbs are ON at the beginning. Bobo knows in advance an n x m binary matrix Ci, j. When the i-th switch is pressed, all the bulbs j satisfying Ci, j = 1 flip its state between ON and OFF. Let f(S) be the number of bulbs staying ON after the switches in set S is pressed. Find the sum of f(S)3 (cubic of f(S)) modulo (109+7) over all 2n possible choices of S.
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