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In 1991, Alon, Babai and Suzuki conjectured that if $n\\geq s+\\max_{1\\leq i\\leq r} k_i$, then $|A|\\leq {n\\choose s}+{n\\choose s-1}+\\cdots+{n\\choose s-r+1}$. In 2000, Qian and Ray-Chaudhuri proved the conjecture under the condition $n\\geq 2s-r$. 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In 1991, Alon, Babai and Suzuki conjectured that if $n\\geq s+\\max_{1\\leq i\\leq r} k_i$, then $|A|\\leq {n\\choose s}+{n\\choose s-1}+\\cdots+{n\\choose s-r+1}$. In 2000, Qian and Ray-Chaudhuri proved the conjecture under the condition $n\\geq 2s-r$. 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