{"raw_statement":[{"iden":"statement","content":"Given two non-negative integers $X$ and $Y$, determine the value of \n$$ \\sum_{i=0}^{X}\\sum_{j=[i=0]}^{Y}[i\\&j=0]\\lfloor\\log_2(i+j)+1\\rfloor $$\nmodulo $10^9+7$ where\n- $\\&$ denotes bitwise AND;\n- $[A]$ equals 1 if $A$ is true, otherwise $0$;\n- $\\lfloor x\\rfloor$ equals the maximum integer whose value is no more than $x$."},{"iden":"input","content":"The first line contains one integer $T\\,(1\\le T \\le 10^5)$ denoting the number of test cases.\n\nEach of the following $T$ lines contains two integers $X, Y\\,(0\\le X,Y \\le 10^9)$ indicating a test case."},{"iden":"output","content":"For each test case, print one line containing one integer, the answer to the test case."},{"iden":"note","content":"For the first test case:\n- Two $(i,j)$ pairs increase the sum by 1: $(0, 1), (1, 0)$\n- Six $(i,j)$ pairs increase the sum by 2: $(0, 2), (0, 3), (1, 2), (2, 0), (2, 1), (3, 0)$\n\nSo the answer is $1\\times 2 + 2\\times 6 = 14$."}],"translated_statement":null,"sample_group":[["3\n3 3\n19 26\n8 17","14\n814\n278"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}