  We measured a set of $\pi^\pm\Sigma^\mp$, $\pi^0\Sigma^0$, and
$\pi^-\Sigma^0$ invariant mass spectra below and above the $\bar{K}N$ mass
threshold in $K^-$-induced reactions on deuteron. We deduced the $S$-wave
$\bar{K}N\rightarrow\pi\Sigma$ and $\bar{K}N\rightarrow\bar{K}N$ scattering
amplitudes in the isospin 0 channel in the framework of a $\bar{K}N$ and
$\pi\Sigma$ coupled channel. We find that a resonance pole corresponding to
$\Lambda(1405)$ is located at 1417.7$^{+6.0}_{-7.4}$(fitting
errors)$^{+1.1}_{-1.0}$(systematic errors) + $[-26.1^{+6.0}_{-7.9}$(fitting
errors)$^{+1.7}_{-2.0}$(systematic errors)]$i$ MeV/$c^2$, closer to the
$\bar{K}N$ mass threshold than the value determined by the Particle Data Group.
