Does touching another person's male organ nullify Wudu?

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Touching another person's male organ nullifies Wudu. The reasoning is that touching another's organ is a sin and more likely to incite desire or lead to discharge than touching one's own, making it more deserving of nullification. Furthermore, some narrations of the supporting Hadith use the general term 'the male organ' (al-dhakar) without specifying one's own.