/**
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⣄⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠉⠛⠶⣤⣸⡇⠀⠀⠀⠀⣀⣤⣶⣶⠒⠒⠒⠶⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠶⢿⣭⣀⡀⢻⡀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠁⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⣴⣞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⢀⡤⠠⡄⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣠⠖⠋⠀⣸⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⢀⣴⠋⢀⢀⡴⠋⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⣼⢿⡄⠀⠀⠀⠀⣆⠀⠉⢦⡀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⣠⠟⠇⠀⠈⠉⠁⠀⣀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢰⠏⠀⠻⣄⠀⠀⠀⠹⣄⣰⠟⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⢀⣀⡖⠀⣰⠏⠀⠀⠀⠀⠀⢀⣼⣿⠋⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡟⠀⠀⠀⠹⣦⠀⠀⠀⠀⠁⠀⣶⠀⠀⣴⠛⢧⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⣩⡟⠀⠀⠈⠉⠀⢀⡟⠀⠀⢀⣀⣠⣤⣾⡿⠗⠒⠚⣿⠠⣤⠀⠀⠀⠀⠀⠀⠀⢸⣿⠓⠒⠲⠶⠶⠾⢷⣤⣀⣀⠀⠀⠙⣧⠀⠹⣆⣼⠃⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⡴⠟⢁⡼⣿⠁⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠉⢠⡾⠋⠀⠀⠀⠀⠸⣆⠙⣧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠻⣆⠉⠁⠀⠀⢹⡄⠀⠈⠁⠀⠀⠘⣷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⡶⠋⢀⡴⠋⢰⡏⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⢻⡄⢸⣷⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣾⡥⠴⠞⠋⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣷⠙⠷⣄⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⣿⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⡄⠀⣼⢏⣀⣤⣶⣦⣤⣶⣶⣶⣶⣶⣿⣿⣾⡆⠀⠈⠻⢦⣼⡇⢰⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣦⠙⢧⣿⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠘⣇⣼⠏⠘⣿⡿⢿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠙⠃⠀⠀⠀⠀⠉⠁⠘⠛⢻⣿⣿⣿⣿⣿⣟⠛⢛⠷⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣷⢹⣆⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⣿⣆⠀⠀⠀⠀⠀⠐⠘⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣰⠟⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣿⠙⣧⣄⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠈⢹⠿⢟⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡿⠀⡀⠀⠀⣼⠃⠀⠀⠀⠀⣀⡾⠋⠀⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⣿⠝⠳⣤⣀⡀⠀⠀⠈⢷⣤⠇⢠⡞⠠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⡾⠃⣠⡾⠃⠀⠀⣀⣤⠾⠋⠀⠀⠀⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣸⣿⠀⠀⠀⠉⠙⠓⡶⠦⠤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢰⡿⠤⠴⠶⣿⠉⠀⠀⠀⠀⠀⢠⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢻⠀⠀⠀⠀⠀⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⡇⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢸⡇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣤⠤⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⢸⠇⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢸⡇⠀⠀⠀⠀⠀⢸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⢺⢀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⠛⣇⠀⠀⠀⠀⠀⠈⣿⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣅⣸⠀⠀⠀⠀⠀⠀⢀⣿⢸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣀⣿⠀⠀⠀⠀⠀⢷⢸⡄⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁⠀⠈⣿⠀⠀⠀⠀⠀⠀⠈⡟⣼⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢿⢿⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠉⠛⠶⢤⣤⣀⣀⠀⣀⡀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⡇⢹⣤⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡿⢸⡆⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⢸⡇⠈⣟⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⢰⡇⠘⡇⠀⠀⠀⠀⠀⠘⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠆⠀⠀⠀⠀⠀⠀⣼⠁⠀⢻⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣼⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠻⣇⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠈⣷⡀⠀⢻⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⡏⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣠⣾⣿⠀⠀⠀⠀⠀⠀⢠⣠⡇⡇⠀⠀⠸⣯⡀⠀⢷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⣼⠁⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣽⡧⠴⢶⣿⣿⠖⠒⠛⠛⠃⠀⠀⠀⠚⠋⠉⠉⠉⠙⠓⠲⢾⡛⠻⣽⠃⠀⠀⠀⠀⠀⠀⢸⣿⣃⠀⠀⠀⠀⢹⣷⠀⠘⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⠃⠀⢸⡏⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣀⠀⠈⠈⢷⠖⠚⠋⠁⢹⡇⠀⢀⣴⠶⠶⢦⣄⣀⣤⡶⠶⠤⠤⠤⠶⠾⠇⢰⡏⠀⠀⠀⠀⠀⠀⠻⣿⣿⣤⡀⠀⠀⠀⠀⢿⣀⠀⠸⣆⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠏⠀⢀⡿⠀⠀⠀⣰⠟⢹⣿⡄⠀⠀⠀⠻⣄⠀⠀⠘⣷⣤⣄⣀⣈⡙⠛⢹⡷⢶⣦⣴⣾⣛⣻⢯⣴⣦⠴⠖⠃⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠹⣆⠀⠀⠸⡞⣧⣆⠀⠹⣄⠀⠀
⠀⠀⠀⠀⢠⡟⠀⠀⡼⠁⠀⠀⣰⠏⠀⠈⣟⣧⠀⠀⠀⠀⢻⣆⠀⠀⠈⣧⡿⠀⠈⠉⠛⠛⣻⣿⡿⢿⣿⡍⠉⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⢀⣴⠀⠀⡾⣿⠁⠀⠀⠘⣧⠀⠀⢿⠘⣟⠀⠀⢻⡄⠀
⠀⠀⢀⣠⡟⠀⢀⡾⠃⠀⠀⣰⡏⠀⠀⠀⣻⠘⣧⠀⠀⠀⠀⢻⣷⡄⠀⠘⢷⡀⠀⠀⠀⠀⠩⣉⠁⠈⣛⡁⠀⠀⠀⠀⠀⠀⣀⣾⠁⠀⠀⣀⣠⣟⠁⠀⣠⣤⡟⠀⠀⠀⠀⠘⣧⡄⠘⡇⠙⣇⠀⠀⠻
*/
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
using namespace std;
using namespace __gnu_pbds;

#define i64 long long
#define ld long double
#define ull unsigned long long
#define bit(n,i) ((n>>i)&1)
#define pii pair<int,int>
#define sz(x) (int)x.size()
#define FOR(i,a,b) for(int i=a; i<=b; i++)
#define FOD(i,a,b) for(int i=a; i>=b; i--)
#define fi first
#define se second
#define pb push_back
#define all(x) x.begin(),x.end()
#define __sumairu__ signed main()
#define die_hard_onimai_fan void seggs()
#define file(name) if(fopen(name".inp","r")){freopen(name".inp","r",stdin);freopen(name".out","w",stdout);}
#define brute(name) if(fopen(name".inp","r")){freopen(name".inp","r",stdin);freopen(name".ans","w",stdout);}
#define TIME (1.0*clock()/CLOCKS_PER_SEC)
#define FAST ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define ai(n) array<int,n>
#define dbg(x) {cout<<#x<<' '<<x<<endl;}
#define dbgF(arr,l,r) {cout<<#arr;FOR(_i,l,r)cout<<' '<<(arr)[_i];cout<<endl;}
#define dbgArr(arr,n) {cout<<#arr;FOR(_i,1,n)cout<<' '<<(arr)[_i];cout<<endl;}
#define el '\n'

template <typename T,typename U>
ostream& operator<<(ostream &os,pair<T,U>p){return os<<"{"<<p.fi<<", "<<p.se<<"}";}
mt19937_64 rd(chrono::steady_clock::now().time_since_epoch().count());

i64 Rand(i64 l,i64 r)
{
    i64 ans=l+rd()%(r-l+1);
    assert(l<=ans&&ans<=r);
    return ans;
}
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
//const i64 base=1e9+7;
//const i64 mod=(1ll<<53)+5;

struct custom_hash {
    static uint64_t splitmix64(uint64_t x) {
        // http://x...content-available-to-author-only...i.it/splitmix64.c
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }

    size_t operator()(uint64_t x) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(x + FIXED_RANDOM);
    }
};

#define i64 long long
#define debug 0

//const int mod=1e9+7;
//const int mod=998244353;
const int inf=1e9;
const i64 infl=1e18;
///check the limits, dummy
const int N=5e5+5;

int n,q;
int t[N],c[N];
vector<pii>query[N];
vector<ai(3)>events[N];
vector<int>adj[N],nadj[N];
int in[N],out[N],timer;
vector<int>key[N],chest[N];
int dp[N],npar[N];
int ans[N],fa[N],sz[N],dep[N],top[N],seq[N];

void dfs_sz(int u){
    if (fa[u] != 0){
        adj[u].erase(find(adj[u].begin(), adj[u].end(), fa[u]));
    }
    sz[u] = 1;
    for(auto &j : adj[u]){
        fa[j] = u;
        dep[j] = dep[u] + 1;
        dfs_sz(j);
        sz[u] += sz[j];
        if (sz[j] > sz[adj[u][0]]) swap(j, adj[u][0]);
    }
}

void dfs_hld(int u){
    in[u] = ++timer;
    seq[timer] = u;
    for(auto j : adj[u]){
        top[j] = (j == adj[u][0] ? top[u] : j);
        dfs_hld(j);
    }
    out[u] = timer;
}

int lca(int u, int v){
    while (top[u] != top[v]){
        if (dep[top[u]] > dep[top[v]]){
            u = fa[top[u]];
        }
        else{
            v = fa[top[v]];
        }
    }
    return dep[u] < dep[v] ? u : v;
}

int jump(int u, int k) {
    if (dep[u] < k){
        return -1;
    }
    int d = dep[u] - k;
    while (dep[top[u]] > d){
        u = fa[top[u]];
    }
    return seq[in[u] - dep[u] + d];
}

int dist(int x, int y){
    int anc = lca(x, y);
    return dep[x] + dep[y] - 2 * dep[anc];
}

bool isAnc(int u,int v){ return in[u]<=in[v]&&out[u]>=out[v];}
bool cmp(int x,int y){ return in[x]<in[y];}

stack<int>st;
int build(vector<int>&node)
{
    int lim=sz(node)-2;

    sort(all(node),cmp);
    FOR(i,0,lim)
    {
        int u=node[i],v=node[i+1];
        node.pb(lca(u,v));
    }
    sort(all(node),cmp);
    node.erase(unique(all(node)),node.end());

    while(!st.empty())st.pop();
    int rt=node[0];
    st.push(rt);
    FOR(i,2,sz(node))
    {
        int u=node[i-1];
        while(!isAnc(st.top(),u))st.pop();

        int p=st.top();
        nadj[p].pb(u);
        st.push(u);
    }
    return rt;
}

struct Fenwick
{
    vector<int>bit;
    int n;
    Fenwick(int n)
    {
        this->n=n+10;
        bit.assign(n+10,0);
    }
    Fenwick(vector<int>a):Fenwick(sz(a))
    {
        FOR(i,0,sz(a)-1)add(i,a[i]);
    }
    int get(int i)
    {
        int ans=0;
        for(++i;i>0;i-=i&-i)ans+=bit[i];
        return ans;
    }
    int get(int l,int r)
    {
        return get(r)-get(l-1);
    }
    void add(int i,int v)
    {
        for(++i;i<n;i+=i&-i)bit[i]+=v;
    }
};

die_hard_onimai_fan
{
    cin>>n>>q;
    FOR(i,1,n)
    {
        int op,x;
        cin>>op>>x;
        if(op==1)key[x].pb(i);
        else chest[x].pb(i);
    }

    FOR(i,2,n)
    {
        int u,v;
        cin>>u>>v;
        adj[u].pb(v);
        adj[v].pb(u);
    }
    dep[1] = 1;
    dfs_sz(1);
    top[1] = 1;
    dfs_hld(1);

    FOR(i,1,q)
    {
        int s,t;
        cin>>s>>t;
        query[in[s]].pb({in[t],i});
    }

    FOR(i,1,n)if(sz(key[i])&&sz(chest[i]))
    {
        auto node=chest[i];
        node.insert(node.end(),all(key[i]));

        int rt=build(node);

        for(int x:chest[i])dp[x]=1;

        auto dfs=[&](auto&&dfs,int u)->void{
            for(int v:nadj[u])
            {
                npar[v]=u;
                dp[v]+=dp[u];
                dfs(dfs,v);
            }
        };
        dfs(dfs,rt);

        auto get=[&](int x,int y){
            int p=lca(x,y);
            return dp[x]+dp[y]-dp[p]-dp[npar[p]];
        };

        for(int a:key[i])for(int b:chest[i])
        {
            int anc=lca(a,b);
            int dis=dep[a]+dep[b]-2*dep[anc];

            vector<pii>p;
            for(int x:key[i])if(dist(a,x)+dist(x,b)==dis)p.pb({dist(a,x),x});

            sort(all(p));

            bool can=1;
            int cnt=0;
            FOR(i,1,sz(p)-1)
            {
                int x=p[i-1].se,y=p[i].se;
                cnt++;
                cnt=max(0,cnt-get(x,y));
                if(cnt==0)
                {
                    can=0;
                    break;
                }
            }
            if(!can||cnt+1!=get(p.back().se,b))continue;

            if(anc==a)
            {
                int t=jump(b,dep[b]-dep[a]-1);
                int l1=1,r1=in[t]-1;
                int l2=out[t]+1,r2=n;
                int l3=in[b],r3=out[b];

                events[l1].pb({l3,r3,1});
                events[r1+1].pb({l3,r3,-1});
                events[l2].pb({l3,r3,1});
                events[r2+1].pb({l3,r3,-1});
            }
            else if(anc==b)
            {
                int t=jump(a,dep[a]-dep[b]-1);
                int l1=1,r1=in[t]-1;
                int l2=out[t]+1,r2=n;
                int l3=in[a],r3=out[a];

                events[l3].pb({l1,r1,1});
                events[r3+1].pb({l1,r1,-1});
                events[l3].pb({l2,r2,1});
                events[r3+1].pb({l2,r2,-1});
            }
            else
            {
                int l1=in[a],r1=out[a];
                int l2=in[b],r2=out[b];

                events[l1].pb({l2,r2,1});
                events[r1+1].pb({l2,r2,-1});
            }
        }

        for(int x:node)
        {
            dp[x]=npar[x]=0;
            nadj[x].clear();
        }
    }

    Fenwick f(n);
    FOR(i,1,n)
    {
        for(auto&&[l,r,v]:events[i])
        {
            f.add(l,v);
            f.add(r+1,-v);
        }

        for(auto&&[x,id]:query[i])ans[id]=f.get(x);
    }

    FOR(i,1,q)cout<<ans[i]<<el;
}

__sumairu__
{
    FAST
    file("");

    int tt=1;//cin>>tt;
    while(tt--)seggs();
    cerr<<"\nTime elapsed: "<<TIME<<" s.\n";
}
/**
5 3
1 2
2 2
1 3
2 3
2 2
1 2
1 3
3 4
3 5
2 4
2 5
4 2
*/