Measurements of branching fractions of D0 → K− 3π + 2π − , D0 → K− 2π + π − 2π0, and D+ → K− 3π + π − π0

Utilizing 7.9 fb−1 of e)e− collision data taken with the BESIII detector at the center-of-mass energy of 3.773 GeV, we report the measurements of absolute branching fractions of the hadronic decays D0 → K−3π)2π−, D0 → K−2π)π−2π0 and D) → K−3π)π−π0. The D0 → K−3π)2π− decay is measured with improved precision, while the latter two decays are observed with statistical significance higher than 5σ for the first time. The absolute branching fractions of these decays are determined to be B(D0→K−3π)2π−)=(1.35±0.23±0.08)×10−4, B(D0→K−2π)π−2π0)=(19.0±1.1±1.5)×10−4, and B(D) → K−3π)π−π0) = (6.57 ± 0.69 ± 0.33) × 10−4, where the first uncertainties are statistical and the second systematic.